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Matrix Multiplication

`C = A*B`

`C = mtimes(A,B)`

is
the matrix product of `C`

= `A`

*`B`

`A`

and `B`

.
If `A`

is an m-by-p and `B`

is a
p-by-n matrix, then `C`

is an m-by-n matrix defined
by

$$C(i,j)={\displaystyle \sum _{k=1}^{p}A}(i,k)B(k,j).$$

This definition says that `C(i,j)`

is the inner
product of the `i`

th row of `A`

with
the `j`

th column of `B`

. You can
write this definition using the MATLAB^{®} colon operator as

C(i,j) = A(i,:)*B(:,j)

`A`

and `B`

, the number
of columns of `A`

must equal the number of rows of `B`

.
Matrix multiplication is `A*B`

is typically
not equal to `B*A`

. If at least one input is scalar,
then `A*B`

is equivalent to `A.*B`

and
is commutative.