The **transpose** of a matrix is a new matrix whose
rows are the columns of the original.
(This makes the columns of the new matrix the rows of the original).
Here is a matrix and its transpose:

The superscript "T" means "transpose".

Another way to look at the transpose is that the
element at row r column c in the original
is placed at row c column r of the transpose.
The element
**a _{rc}** of the original matrix
becomes element

Usually we will work with square matrices, and it is usually square matrices that will be transposed. However, non-square matrices can be transposed, as well:

What is: