Question

Is it possible to take a dot product of two matricies?

I know that to multiply two matricies, you essentially take the dot product of the corrosponding rows of one matrix and the columns of a second matrix (given the dimensions permit). But what happens when you try to take one matrix and dot it with another, or if that is even defined?

Answer 1

if you look up the innerproduct of matricies you will see the matrix version of the dot product. The "dot product" is an innerproduct on two vectors.

Answer 2

ther eis a much more general way of thinking about the inner product. .
the inner product satisfies these properties

<u+v,w> = <u,w> + <v,s>
<av,w> = a<v,w>
<v,s> = <w,v>
<v,v> >= 0 and dqual iff v = 0

where v and w are objects and a is a scalar

Answer 3

that should say <v,w> = <w,v>

Answer 4

so yes there is an "dot product" with matricies, and it acts exactly how you would want it to...
multiply a_i_j * b_i_j for all i j and add them up.