## Transposing a Matrix

February 7, 2020

Let's take a matrix representing some sort of column vector.

When we *transpose* a matrix, we want to find a new matrix such that the *columns* of matrix become the *rows* of the matrix .

To find , we then need to take the columns in , and assign them as rows to .

For matrix :

We can then take each column, and transpose them individually to rows in .

This also works the other way around. You can also transpose the matrix by taking *every row* of the matrix, and assigning it as the *column* of the transposed matrix.

Suppose matrix . Then . Then, .

Notice that we are not just limited to transposing square matrices.