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).

(“Transpose” 2022)

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

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

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

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