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).

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

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

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

## References

“Transpose.” 2022.

*Wikipedia*, June. https://en.wikipedia.org/w/index.php?title=Transpose&oldid=1094750580.