In linear algebra, the transpose of a matrix is an operator which flips a matrix over its diagonal; that is, it switches the row and column indices of the matrix $$A$$ by producing another matrix, often denoted by $$A^{\textsf{T}}$$ (among other notations).

$$A = \begin{bmatrix}1 & 2 \\ 3 & 4 \\ 5 & 6\end{bmatrix}$$

$$A^{\textsf{T}} = \begin{bmatrix}1 & 3 & 5 \\ 2 & 4 & 6\end{bmatrix}$$

$$(A^{\textsf{T}})^{\textsf{T}} = A$$