MATLAB Basics-Part1

MATLAB Basics-Part1
Learning The Basics Of Matlab
Eng. Elaf Ahmed Saeed

What is MATLAB?
 Matlab is basically a high level language which has many
specialized toolboxes for making things easier for us.
 How high?
Matlab
High level
languages such as
C, Pascal etc.
Assembly

What is MATLAB?
 Matlab stands for MATrix LABoratory.
 The first version of MATLAB was produced in the mid 1970s as a
teaching tool. MATLAB started as an interactive program for doing
matrix calculations.
 MATLAB has now grown to a high level mathematical language that
can solve integrals and differential equations numerically and plot a
wide variety of two and three Dimensional graphs.
 The expanded MATLAB is now used for calculations and simulation
in companies and government labs ranging from aerospace, car
design, signal analysis through to instrument control and financial
analysis.
 In practice, it provides a very nice tool to implement numerical
method.

MATLAB Environment
 When you start MATLAB, the desktop appears in its default layout.

MATLAB Environment
 The desktop includes these panels:
• Current Folder — Access your files.
• Command Window — Enter commands at the command line,
indicated by the prompt (>>).
• Workspace — Explore data that you create or import from files.

MATLAB Startup Window Workspace
• View program variables
• Double Click on a variable
Command Window
Type Command
Current folder
View folders and m-files
Command History
• View past command
• Save a whole session using
diary.

MATLAB Components
MATLAB Workspace
Handle graphic Simulink
Toolboxes MATLAB Compiler

Command Window
 After starting MATLAB, the Command window will open with the
Command prompt being displayed: >>
 The calculator mode of MATLAB operates in a sequential fashion as
you type in Commands line by line. For each command, you get a
result.
 For example, if you type >> 55 – 16
MATLAB will display the result
ans=
39 (Try >> ans + 10)

Tip
 Using the up-arrow key, you can go back to any command that you
entered. Press the up-arrow until you get back the line.
>> b * a
 Alternatively, you can type b and press the up-arrow once and it will
automatically bring up the last command beginning with the letter b. the
up-arrow shortcut is a quick way to fix errors without having to retype the
entire line.

MATLAB Installation
Version 2018

Step1
 Select (install manually…..)  Next

Step 2
 Select (yes)  Next

Step 3
 Select (I have file installation key)

Step 4
 Copy the from the text file.
Copy
Key

Step 6
 Select Typically  Next

Step 7
 Select path to installation  Next

Step 9
 Download window. This step takes some time to install the program.

Step 10
 After install complete select (Activate manually without internet)
Next

Step 11
 Enter the path of file license.

Step 11
 The file license with the folder installation.

Step 13
 If the shortcut not found you can found it from:
C  program files  MATLAB  R2018a  bin  matlab

Step 13
 If the short cu not found you can found it from:
C  program files  MATLAB  R2018a  bin  matlab

Step 14
 If the MATLAB not open do the following:
Copy the (license_standalone.lic) and paste it in the folder (licences)
In MATLAB folder in C.

What is Assignment?
 Assignment refers to assign values to variable
names. This results in the storage of the values in
the memory location corresponding to the
variables name.
>> a = 5

Scalars
 In MATLAB a scalar is a variable with one row and one column.
Scalars are the simple variables that we use and manipulate in
simple algebraic equations.
 Creating scalars
To create a scalar you simply introduce it on the left hand side of an
equal sign.
>> x = 1;
>> y = 2;
>> z = x + y;

Scalars
 Scalar operations
MATLAB supports the standard scalar operations using an obvious
notation. The following statements demonstrate scalar addition,
subtraction, multiplication and division.
>> u = 5;
>> v = 3;
>> w = u + v
>> x = u - v
>> y = u * v
>> z = u/v

Scalars
 >> a = 4
Note how the assignment echo prints to confirm what you have done:
a =
4
 Echo printing is a characteristic of MATLAB. It can be suppressed by
terminating the command line with the semicolon (;)
>> A = 6;
 You can type several commands on the same line by separating them
with commas or semicolons. For example,
>> a = 4, A = 6; x = 1;
a =
4

Note
 MATLAB Treats names in a case-sensitive
manner. That is, the variable a is not the same as
A. To illustrate this, enter
>> a
And then enter
>> A

Complex Number
 We can assign Complex Values to variables, since MATLAB handles
complex arithmetic automatically. The unit imaginary number −𝟏 is
preassigned to the variable i.
>> x = 2+i*4
x =
2.0000 + 4.0000i
 It should be noted that MATLAB allows the symbol j to be used to
represent the unit imaginary number for input. However, it always uses
an i for display. For example,
>> x = 2+j*4
x=
2.0000+4.0000i

Complex Number
 Function with complex numbers:

Complex Number
 Examples:
>> x=3+4i
ans=
3.0000 + 4.0000i
>> real(x)
ans=
3
>> imag(x)
ans=
4
>> abs(x)
ans=
5

Complex Number
 Examples:
>> angle(x)
ans=
0.9273
>> conj(x)
ans=
3-4i

Predefined variables
 There are several predefined variables, for examples, pi.
>> pi
ans=
3.1416
 >> exp(1)
ans=
2.7183

Format type
 Note how MATLAB displays four decimal places. If you desire
additional precision, enter the following:
>> format long
 Now when pi is entered the result is displayed to 15 significant
figures:
>> pi
ans=
3.14159263558979

Format type
 If we want to go back to the four digits after coma write:
>> Format short
>> pi
ans=
3.1416
 The following is a summary of the format commands you will employ
routinely in engineering and scientific calculations. They all have the
syntax: format type

Format type
Type Result Example
short Scaled fixed-point format with 5 digits. 3.1416
long Scaled fixed-point format with 15 digits
for double and 7 digits for single.
3.14159265358979
Short e Floating point format with 5 digits. 3.1416e+000
Long e Floating point format with 15 digits for
double and 7 digits for single.
3.141592653589793e+000
Short g Best of fixed or floating point format with
5 digits.
3.1416
Long g Best of fixed or floating point format with
15 digits for double and 7 digits for
single.
3.14159265358979
Short eng Engineering format with at least 5 digits
and a power that is a multiple of 3.
3.1416e+000
Long eng Engineering format with at least 16 digits
and a power that is a multiple of 3.
3.14159265358979e+000
bank Fixed dollars and cents 3.14

Exercise
 Given x=2
y=x+2
z=x+y
1/ Type these simple statements to find the value of y and z.
2/ Try to put the variables in one row and get the answer.
3/ Hide the result of x , y and get only the result of z.

Basic Math Operations
 Mathematical operations in MATLAB can be performed on both
scalars and arrays.
 The common operators, in order of priority, are:
Symbol Meaning Example
^ Exponentiation 4^2=8
- Negation (unary operation) -8=-8
*
/
Multiplication and Division 2*pi = 6.2832
Pi/4 = 0.78554
Left Division 62 = 0.3333
+
-
Addition and
Subtraction
3+5=8
3-5 = -2

 Order of Operations
• The order of operations is set first by parentheses, then by the default order
given above:
 Y= -4 ^ 2 gives y= -16
Since the exponentiation happens first due to its higher default priority, but
 Y = (-4) ^ 2 gives y = 16
Since the negation operation on the 4 takes place first.

 Examples
1. Compute (2+3-9)*7^2/4
ans = -49
2.
1
2+32 +
4
5
x
6
7
In MATLAB it becomes
>> 1/(2+3^2) + 4/5 * 6/7
ans = 0.7766
Or, if parentheses are missing,
>> ½+3^2 + 4/5 * 6/7
ans = 10.1857
3. >> -5 / (4.8) + 5.32) ^ 2
ans = -0.0488

 Calculations can also involve complex quantities. x = (2+4i) and y = (16):
>> 3 * x
ans = 6.0000 + 12.0000i
>> x ^ 2
ans = -12.0000 + 16.0000i
>> x + y
ans = 18.0000 + 4.0000i
>> (3 + 4i) * (3 – 4i)
ans = 6.1230e-017

Relational Operations
 A > B The result is true if A is greater than B, and is false otherwise.
 A < B The result is true if A is less than B, and is false otherwise.
 A >= B The result is true if A is grater than or equal to B, and is false otherwise.
 A <= B The result is true if A is less than or equal to B, and is false otherwise.
 A == B The result is true if A is equal to B, and is false otherwise.
 A ~= B The result is true if A is not equal to B, and is false otherwise.
Example:
>> a = 5; b = 2;
>> x = a > b ;
x = 1 (true)
>> x = (a == b);
x = 0 (false)

 Note
Many users confuse the double equality sight (==) used in relational
tests with the equality sign (=) used in assignments. When a user uses
(=) instead (==), MATLAB usually reports that an expected relational
operator wasn’t found.

 The table summary of relational operators in MATLAB.
Example Operator Relational
X == 0 == Equal
Unit ~= ‘m’ ~= Not equal
A < 0 < Less Than
S > t > Greater Than
3.9 <= a/3 <= Less than or equal to
R >= 0 >= Greater than or equal to

Logical Operations
 The table that summarize the logical operation in MATLAB.
Operator Operation
& Logical AND
&& Logical AND with shortcut evaluation
| Logical OR
|| Logical OR with shortcut evaluation
xor Logical exclusive OR
~ Logical NOT

Logical Operations
 A truth table summarize the possible outcomes for logical operators
employed in MATLAB. The order of priority is shown at the top of
the table.
Highest Lowest
X Y ~X X&Y X|Y
T T F T T
T F F F T
F T T F T
F F T F F

Logical Operations
• ~x (NOT): true if x is false (or zero); false otherwise.
• x & y (NND): true if both x and y are true (or non-zero).
• x | y (OR): true if either x or y are true (or non-zero).
 Priority can be set using parentheses. After that, mathematical expressions
are highest priority, followed by relational operators, followed by logical
operators. All things being equal, expression are performed from left to
right.
 Not is the highest priority logical operator, followed by AND and finally
OR.

Logical Operations
 Examples:
>> 1 & 1
ans = 1
>> 1 | 0
ans = 1
>> 0 & 0
ans = 0
>> ~1
ans = 0

Built-in Functions
 MATLAB and its toolboxes have a rich of collection of built-In
functions. You can use online help to find out more about them. For
example, if you want to learn about the log function:
>> help log
LOG Natural logarithm.
LOG(x) is the natural logarithm of the elements of x.
Complete results are produced if x is not positive.
See also log2, log10, exp, logm.

Built-in Functions with vector and
Matrix
 One of the important properties of MATLAB’S built-in functions is
that they will operate directly on vector and matrix quantities. For
example, try
>> A = [1 2 3; 4 5 6; 7 8 9]
>> log(A)
ans =
0 0.6931 1.0986
1.3863 1.6094 1.7918
1.9459 2.0794 2.1972

Matrix
 You will see that the natural logarithm function is applied in array
style, element by element, to the matrix A. Most functions, such as
sqrt, abs, sin, acos, tanh, and exp, operate in array fashion.
>> sqrt(A)
ans =
1.0000 1.4142 1.7321
2.0000 2.2361 2.4495
2.6458 2.8284 3.0000

Matrix
 Length and Size functions
 The length and size functions in MATLAB are used to find dimensions of
vector and matrices. The length function returns the number of elements in
a vector. The size function returns the number of rows and columns in a
vector or matrix. For example
>> vec(-2:1)
vec = -2 -1 0 1
>> length(vec)
ans = 4
>> size(vec)
ans = 1 4

Matrix
 Note
The length function will return either the number of rows or the number of
columns, whichever is largest.
 we can create a matrix of zeros with the same size as another matrix. For a
matrix variable vec, the following expression would accomplish this:
zeros(size(vec))
The size function returns the size of the matrix, which is then passed to the
zeros function, which then returns a matrix of zeros with the same size as vec.
 What would be produced by the following command line:
>> rand(size(vec))

Round-off Functions
 There are several functions for rounding. For example, suppose that we
enter a vector:
>> x = [-1.6-1.5-1.41.4 1.5 1.6]
• The round function rounds the elements of x to the nearest integers:
>> round(x)
ans = -2 -2 -1 1 2 2
• The ceil (short for ceiling) function rounds to the nearest integers toward
infinity:
>> ceil(x)
ans = -1 -1 -1 2 2 2

Round-off Functions
• The floor function rounds down to the nearest integers toward minus
infinity:
>> floor(x)
ans = -2 -2 -2 1 1 1

Built-In Help Functions
 The built-in help function can give you information about both what
exists and how those functions are used:
• help elmat will list the elementary matrix creation and manipulation
functions, including functions to get information about matrices.
• help elfun will list the elementary math functions, including trig,
exponential, complex, rounding, and reminder functions.
 The built-in lookfor command will search help files for occurrences
of text and can be useful if you know a function’s purpose but not
its name. (to stop search click (ctrl+c))

Summary of Built-in Functions in
MATLAB
 General Functions
Function Used to
who List current variables.
whos List current variables in details
clear x Clear variable x from memory
open Open new file
figure(n) Opens new figure numbered n
close Closes last figure
Close all Closes all figures
dir List files in directly
format Set output format
help To know any command and
example
lookfor To search for command
exit Quits MATLAB

MATLAB
 Elementary Math (Arithmetic Operations) Basic Arithmetic
• Addition
• Subtraction

MATLAB
• Multiplication
• Division

MATLAB
• Powers
• Transpose

MATLAB
• Modulo Division and Rounding

MATLAB
 Elementary Math (Arithmetic Operations) Trigonometry
• Sine

MATLAB
• Cosine

MATLAB
• Tangent

MATLAB
• Cosecant

MATLAB
• Secant

MATLAB
• Cotangent

MATLAB
 Elementary Math (Arithmetic Operations) Exponents and
Logarithms

MATLAB
 Elementary Math (Arithmetic Operations) Complex Numbers

MATLAB
 Elementary Math (Linear Algebra) Matrix Operations

MATLAB
 Elementary Math (Random Number Generation)

MATLAB
 Elementary Math (2-D and 3-D Plots) Line Plots

MATLAB
 Elementary Math (2-D and 3-D Plots) Function Plots

MATLAB
 Elementary Math (Labels and Annotations) Labels

MATLAB
 Elementary Math (Labels and Annotations) Multiple Plots

MATLAB
 Elementary Math (Help and Support)

MATLAB
For more learn :
https://uk.mathworks.com/help/matlab/referencelist.html?type=functio
n&s_tid=CRUX_topnav

Vectors and Matrices in MATLAB

Arrays, Vectors, and Matrices
Introduction
 An array is a collection of values that are represented by a single
variable name.
 MATLAB can automatically handle rectangular arrays of data-one-
dimensional arrays are called vectors and two-dimensional arrays are
called matrices.
 Arrays are set off using square bracket [ ] in MATLAB.
 Entries within a row are separated by space or commas.
 Rows are separated by semicolons.

Array Examples
 Row Vector
>> a=[1 2 3 4 5 ]
a=
1 2 3 4 5
 Columns Vector
>> b = [2;3;6;8;10]
b=
2
4
6
8
10

Use of Vector
 MATLAB indexing starts with 1, not 0.
• We will not respond to any emails where this is the problem.
 A(n) returns the 𝑛 𝑡ℎ
element.
A=[13 5 9 10]
 The index argument can be a vector. In this case, each element is
looked up individually, and return as a vector of the same size as
the index vector.
A(1)
A(2) A(3) A(4)

Matrices
 A 2-D array, or matrix, of data is entered row by row, with spaces (or
commas) separating entries with row and semicolons separating the
rows:
>> A= [1 2 3; 4 5 6; 7 8 9]
A=
1 2 3
4 5 6
7 8 9

Useful Array Commands
 The transpose operator (apostrophe) can be used to flip an arrays
over its own diagonal. For example, if b is a row vector, b’ is a
column vector containing the complex conjugate of b. (Try b’)
 The command window will allow you to separate rows by hitting the
enter key – script file and functions will allow you to put rows on
new lines as well. (Retype the matrix A as describe above).
 The who command will report back used variable names; whos will
also give you the size, memory, and data types for the arrays.

Accessing Matrix Entries
 Individual entries within array can be both read and set using either
the index of the location in the array or the row and column.
 The index value starts with 1 for the entry in the top left corner of an
array and increases down a column – the following shows the
indices for a 4 row, 3 column matrix:
1 5 9
2 6 10
3 7 11
4 8 12

Accessing Matrix Entries(Cont)
 Accessing some matrix C:
C=
2 4 9
3 3 16
3 0 8
10 13 17
C(2) Would report 3
C(4) Would report 10
C(13) Would report an error!

Accessing Matrix Entries(Cont)
 Entries can also be access using the row and column:
C(2,1) Would report 3
C(5,1) Would report an error!
C(4,:) Would report the whole fourth raw.
C(:,2) Would report the whole second column.

Array & Matrix Creation-Built In
 There are several built-in functions to create arrays and matrices:
• zeros(r,c) Will create an r row by c column matrix of zeros.
• zeros(n) Will create an n by n matrix of zeros.
• ones(r,c) Will create an r row by c column matrix of ones.
• ones(n) Will create an n by n matrix of ones.
Try… rand(n) and rand(r,c)
 help elmat has, among other things, a list of the elementary
matrices.
Try… zeros(3) , ones(2)

Array Creation-Colon Operator
 The colon operator : is useful in several contexts. It can be used to create a
linearly spaced array of points using the notation.
Start:diffval:limit
Where start is the first value in the array, diffval is the difference between
successive values in the array, and limit is the boundary for the last value
(though not necessary the last value).
>> 1:6:3
ans=
1.0000 1.6000 2.2000 2.8000

 Note
 If diffval is omitted, the default value is 1:
>> 3:6
ans=
3 4 5 6
 To create a decreasing series, diffval must be negative:
>> 5:-1.2:2
ans=
5.0000 3.8000 2.6000

(Cont)
 If start+diffval>limit for an increasing series or
start+diffval>limit foe decreasing series, an empty matrix is
returned:
>> 5:2
ans=
Empty matrix: 1-by-0
 To create a column, transpose the output of the colon operator, not
the limit value; that is, (3:6)’ not 3:6’

Array Creation- linespace
 To create a row vector with a specific number of linearly spaced
points between two numbers, use the linspace command
 Linspace (x1,x2,n) will create a linearly spaced array of n points
between x1 and x2
>> linspace(1, 1, 6)
ans=
0 0.2000 0.4000 0.6000 0.8000 1.0000
 If n is omitted, 100 points are created.
 To generate a column, transpose the output of the linspace
command.

Array Creation- linspace
(Cont)
>> linspace(0,1,6)’
ans=
0
0.2000
0.4000
0.8000
1.0000

Exercise(1)
 Use the linspace function to create vectors identical to the following
created with colon notation:
 t = 5:6:30
 x = -3:4
 Homework
y = -4:2

Array Creation- logspace
(Cont)
 To create a row vector with a specific number of logarithmically
spaced points between two numbers, use the logspace command.
 Logspace(x1, x2, n) will create a logarithmically spaced array of n
points between 10 𝑥1
and 10 𝑥2
.
>> logspace (-1, 2, 4)
ans=
0.1000 1.0000 10.0000 100.0000
 If n is omitted, 100 points are created.
 To generate a column, transpose the output of the logspace
command.

Character Strings & Ellipsis
 Alphanumeric are enclosed by apostrophes (‘)
>> f= ‘ Mailes‘
>> s = ‘Davis’
Concatenation: passing together of strings
>> x= [f s]
x=
Miles Davis
Ellipsis (…): Used to continue long lines
>> a = [1 2 3 4 5 …
6 7 8]
a=
1 2 3 4 5 6 7 8

Character Strings & Ellipsis
 You cannot use an ellipsis within single quotes to continue a string.
But you can piece together shorter strings with ellipsis.
>> quote = [‘Hello Word’ …
‘I am a Teacher’]
quote =
Hello Word I am a Teacher

Vector-Matrix Calculations
 MATLAB can also perform operations in vectors and matrices.
 The * operator for matrices is defined as the product or what is commonly called
“matrix multiplication.”
• The number of columns of the first matrix must match the number of rows in the
second matrix.
• The size of the result will have as many rows as the first matrix and as many
columns as the second matrix.
• The exception to this is multiplication by a 1x1 matrix, which is actually an array
operation.
 The ^ operator for matrices result in the matrix being matrix-multiplied by itself a
specified number of times.
• Note – in this case, the matrix must be square! Why?
Because, matrix-multiplied by itself .

Element-by-Element Calculations
 At time, you will want to carry out calculation item by item in a matrix or
vector. The MATLAB manual calls these array operations. They are also
often referred to as element-by-element operations.
 MATLAB defines .* and ./ (note the dots) as the array multiplication and
array division operators.
• For array operations, both matrices must be the same size or one of the
matrices must be 1x1.
 Array exponentiation (raising each element to a corresponding power in
another matrix) is performed with .^
 Again, for array operations, both matrices must be the same size or one of
the matrices must be 1x1.

Notes
 To define the matrix using another matrix:
B=[1.5, 3.1]; S=[3.0 B]; This is equal to S=[3.0 1.5 3.1]
 Changing the value in a matrix:
Lets consider that we have matrix S, S(2)=1.5
To change the second value of S from 1.5 to -1.0
We type: S(2) = -1.0;

Simple Practice
 a= 1 2 3
b= 2
4
6
c= 78 9
Try
 a+b {is it possible?!} what about a+c
 a.c
 b.a
 a/pi
 a^2

Examples about Vectors
 1- >> x = [12 13 5 8]
x (2:3); a = [ 13 5];
b = x(1 : end-1);  b = [12 13 5];
 2- >> a[1 : 5]
a =
1 2 3 4 5
 3- >> a = [1 : 2 : 5]
a =
1 3 5

Examples about Vectors
 4- >> b = prod (x)
b =
120
 5- >> a = [5E-1 7E-2 9e-4]
a=
0.5000 0.0700 0.0009

Examples about Special Matrices
 1- >> a = zeros (2,3)
a =
0 0 0
0 0 0
 2- >> a = ones (2,3)
a =
1 1 1
1 1 1

 3- >> eye(4)
a = 10 0 0
0 1 0 0
0 0 1 0
0 0 0 1
 4- >> x = [1 2; 1 6]
x =
1 2
1 6
y=
1.5000 -0.5000
-0.2500 0.2500

 5- >> r = magic(4)  generate a random matrix according to the
number between Parentheses.
 6- >> x = [1 2; 4 2]
>> max(x)
ans =
4 2
>> max (max(x))
ans =
4

 7- >> x = [1 2 3; 4 5 6];
>> reshape(x,2,3)
ans =
1 2 3
4 5 6
>> reshape(x,3,2)
ans =
1 5
4 3
2 6

 8- >> fliprl(x)
ans =
3 2 1
6 5 4
 9- >>flipud(x)
ans =
4 5 6
1 2 3
 >> size(x)
ans =
2 3

Matrix Manipulation Functions
Function Used to
zeros Create an matrix of all zeros.
length Length of matrix.
ones Create an matrix of all ones.
eye Identity matrix.
rand Uniformly distributed random number.
size Return matrix dimension.
Fliprl Flip matrices left-right.
Flipud Flip matrices up and down.
size Dimension of matrix.

Examples about operation on
Matrices
 1- Transpose
>> a = [1 2; 3 4]
a=
1 2
3 4
>> a’
ans =
1 3
2 4

Matrices
>> transpose (a)
ans =
1 3
2 4
>> rot90 (a)
ans =
2 4
1 3
>> rot90(rot90(a))  180 deg.
ans =
4 3
2 1

Matrices
 2- Addition
must be the two matrices have the dimention.
>> a = [1 2; 3 4];
>> b = [1 2; 3 4];
>> a + b
ans =
2 4
6 8
>> a + 2
ans =
3 4
5 6

Matrices
 3- Multiplication
>> a = [1 2; 3 4];
>> b = [1 2; 3 4];
>> a * b
ans =
7 10
15 22
>> 2 * a
ans=
2 4
6 8

Matrices
>> C = ones(2,4)
C =
1 1 1 1
1 1 1 1
>> a * C
ans =
3 3 3 3
7 7 7 7

Matrices
 4- Division
>> a = [1 2; 3 4];
>> b = [1 2; 3 4];
>> a/b
ans =
1 0
0 1
Or: >> a*inv(b)
ans =
1.0000 0.0000
0.0000 1.0000

Matrices
 5- Dot Multiplication
>> a = [1 2; 3 4];
>> b = [1 -1; 2 -2];
>> c = a .* b
ans =
1 -2
6 -8

Matrices
 6- Dot Division
>> c = a ./ b
 7- Dot Power
>> c = a .^ b
 8- Inverse
>> a = [1 2; 3 4]
>> b = inv (a)
b = -2.0000 1.0000 
1.5000 -0.5000
Or:
>> b = a ^ -1
b =
-2.000 1.000
1.5000 -0.5000

Matrices
 9- Determinant
>> a = det (a)
d = 0
 10- Power
>> a = [1 2; 3 4]
a =
1 2
3 4
>> b = a ^2
b =
7 10 
15 22
• The matrix must be square.
• a .^2 is equivalent a *a

Matrices
 11- Summation
- >> a = [1 3 5]
a = 1 3 5
>> s = sum(a)
s =
9
- >> a = [12; 3 4];
>> sum(sum(a))
ans =
10

Matrices
 12- Rank
1- rank(A) provides an estimate of the number of linearly independent rows or
columns of a matrix A.
2- trace (A) sum of the diagonal elements of A.
>> A = [1 2 5; 0 1 7; 2 3 4]
>> rank (A)
ans =
3
>> trace (A)
ans =
6

Matrix Sub-scripting
 P = pascal(n) returns a Pascal’s Matrix of order n. P is a symmetric
positive definite matrix with integer entries taken from Pascal's triangle.
The inverse of P has integer entries.
 >> p = pascal(5)
a =
1 1 1 1 1
1 2 3 4 5
1 3 6 10 15
1 4 10 20 35
1 5 15 35 70

Matrix Sub-scripting (Cont)
>> a(3, 2)
ans =
3
>> a (8)
ans =
3
>> a (: , 3)
1
3
6
10
15

>> a (3:4 , 3:4)
ans =
1
3
>> a (1:5, 3)
ans =
1
3
6
10
15

>> [a(7) a(17) ; a(9)]
z =
2 4
4 20
Or:
>> z = [a(2,2) a(2,4); a(4,2) a(4,4)]
z =
2 4
4 20

>> a (:, [1 2])
ans=
1 1
1 2
1 3
1 4
>> a (: , 5) = [ ]  Delete the rows of the specific column.
1 1 1 1
1 2 3 4
1 3 6 10
1 4 10 20
1 5 15 35

>> a (3 , :) = [ ]  delete the third row
a=
1 1 1 1
1 2 3 4
1 4 10 20
1 5 15 35

Concatenation Examples
>> x = [1 3 4 5]
x=
1 3 4 5
>> y = [x 1]
y =
1 3 4 5 1
>> y = [x; 2*x; 3*x]
y =
1 3 4 5
2 6 8 10
3 9 12 15

Concatenation Examples
>> z = [2 3 4 5]
z =
2 3 4 5
>> y = [x; 2*x; 3*x; z]
y =
1 3 4 5
2 6 8 10
3 9 12 15
4 3 4 5

Matrix Manipulation Functions
Function Syntax Description Example
Determinant B=det(A) B(a number) is the
determinant of A (a
square Matrix)
B=det(A)
Inverse D=inv(A) D (a square matrix) is
the inverse of A (a
square matrix)
A=inv(B*C)
Rank N=rank(A) N (a number) is the rank
of A (a matrix)
h= rank(A) - 1
Diagonal A=diag(c) A is the main diagonal
elements of c.
A= 2+diag(8)
Sum A=sum(B) A is the sum of all
elements of B if it is a
vector or sum of column
of B if it is a matrix.
A=sum (x)
Transpose A= transpose(b) A is the non conjugate
transpose of b.
A= transpose(b)
Or
(A = b’)

Exercise (2)
 Write the MATLAB commands that will create the following matrices:
 Now try to find (if the answer exist check that it is correct by hand)
>> b + c ………………………………………………………….
>> b - 2*c ………………………………………………………..
>> a + b ………………………………………………………….

Exercise (2)
 Calculate b*a by hand and then use MATLAB to check your answer.
 Now check that MATLAB gives the same results for b^3 and b*b*b (you don’t
need to do these by hand)
 Does the product a*b make sense?
 How can we display the second raw of matrix a?
 Change the value of c(4) to 10.

Exercise (3)
 Find an efficient way to generate the following matrix:
mat=
10 20 30 40
-6 -4 -2 0
Then, give an expression that will refer to the first two column.

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