# we know that (n X p) matrix when multilied with (p X m) matrix yeild.pdf

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we know that (n X p) matrix when multilied with (p X m) matrix yeilds (n X m ) matrix. u -> ( n X 1) (u^T) -> ( 1 X n) v- >(n X 1) (v ^T) -> ( 1 X n) => uv^T= (n X1 ) *( 1 Xn)= (n X n) =>u^Tv= (1 Xn )*( n X 1)= (1 X 1) =>vTu= (1 X n) *( nX1)=(1 X1) =>vu^T= (n X1)*(1 X n)= ( nX n). i terms of size , 1st and 4th are equal . similarly 2nd and 3rd are equal. Solution we know that (n X p) matrix when multilied with (p X m) matrix yeilds (n X m ) matrix. u -> ( n X 1) (u^T) -> ( 1 X n) v- >(n X 1) (v ^T) -> ( 1 X n) => uv^T= (n X1 ) *( 1 Xn)= (n X n) =>u^Tv= (1 Xn )*( n X 1)= (1 X 1) =>vTu= (1 X n) *( nX1)=(1 X1) =>vu^T= (n X1)*(1 X n)= ( nX n). i terms of size , 1st and 4th are equal . similarly 2nd and 3rd are equal..

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### we know that (n X p) matrix when multilied with (p X m) matrix yeild.pdf

• 1. we know that (n X p) matrix when multilied with (p X m) matrix yeilds (n X m ) matrix. u -> ( n X 1) (u^T) -> ( 1 X n) v- >(n X 1) (v ^T) -> ( 1 X n) => uv^T= (n X1 ) *( 1 Xn)= (n X n) =>u^Tv= (1 Xn )*( n X 1)= (1 X 1) =>vTu= (1 X n) *( nX1)=(1 X1) =>vu^T= (n X1)*(1 X n)= ( nX n). i terms of size , 1st and 4th are equal . similarly 2nd and 3rd are equal. Solution we know that (n X p) matrix when multilied with (p X m) matrix yeilds (n X m ) matrix. u -> ( n X 1) (u^T) -> ( 1 X n) v- >(n X 1) (v ^T) -> ( 1 X n) => uv^T= (n X1 ) *( 1 Xn)= (n X n) =>u^Tv= (1 Xn )*( n X 1)= (1 X 1) =>vTu= (1 X n) *( nX1)=(1 X1) =>vu^T= (n X1)*(1 X n)= ( nX n). i terms of size , 1st and 4th are equal . similarly 2nd and 3rd are equal.
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