Transpose

A transpose operation allows you to turn a $m\times n$ matrix into an $n\times m$ matrix.

To perform a transpose, imagine taking the top left and bottom right corners and flipping the matrix over. The top row from left to right should become the first column from top to bottom and so on.

Identities

• $(A^T)^T = A$
• $(cA)^T = cA^T$
• $(A+B)^T = A^T + B^T$
• $(AB)^T = B^TA^T$ pay attention to this
• $(A^{-1})^T = (A^T)^{-1}$