Matrix multiplications always have the origin as a fixed point.

Using this system, translation can be expressed with matrix multiplication.

For example, a very large matrix multiplication would take only a few seconds on a machine that was much less powerful than those today.

This is a group with matrix multiplication as operation.

It plays a role in research of fast matrix multiplication algorithms.

That is, the order of the matrix multiplication matters.

Then the bra can be computed by normal matrix multiplication.

This approach drastically reduces the necessary amount of matrix multiplication.

This identity can be easily proved using the matrix multiplication representation.

This follows from the distributivity of matrix multiplication over addition.

Many large mathematical operations on computers end up spending much of their time doing matrix multiplication.

Matrix multiplication also does not necessarily obey the cancellation law.

One example of this might be (small) matrix matrix multiplications.

Then, where is the resultant of the matrix multiplication.

In matrix multiplication, there is actually a distinction between the cross and the dot symbols.

Other rotation matrices can be obtained from these three using matrix multiplication.

An example of a systolic algorithm might be designed for matrix multiplication.

Some modern ciphers use indeed a matrix multiplication step to provide diffusion.

Square nonnegative matrices of a given size with matrix multiplication.

In order to do this, we expand the definition of matrix multiplication:

Or, for those less comfortable with matrix multiplication.

The matrix multiplication can be calculated by the following algorithm:

By the definition of matrix multiplication, we have .

The group operation is that of matrix multiplication.

We have many options because matrix multiplication is associative.