The **transpose** of a matrix is a new matrix whose
rows are the columns of the original
(which makes its columns 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 if the original is placed at row c column r of the transpose. We will usually work with square matrices, and it is usually square matrices that will be transposed. However, non-square matrices can be transposed, as well: