The vector outer product , takes an column vector, an column vector, and returns an matrix obtained by multiplying each element of by each element of In particular, ijij The product is also...

The vector outer product ,
takes an

column vector,

an

column vector,

and returns an

matrix obtained by multiplying each element of

by each element of

In particular,

<sub>ij

i

j</sub>

The product

is also called the tensor product. The outer product computes the inertial tensor in rigid body dynamics, performs transform operations in digital signal processing and digital image processing, and has applications in statistics.

Show that

^T

Show that if
then