2.5: The Transpose - Mathematics LibreTexts
https://math.libretexts.org/Bookshelves/Linear_Algebra/A_First_Course_in_Linear_Algebra_(Kuttler)/02%3A_Matrices/2.05%3A_The_Transpose
WEBSep 17, 2022 · Definition \(\PageIndex{1}\): The Transpose of a Matrix . Let \(A\) be an \(m\times n\) matrix. Then \(A^{T}\), the transpose of \(A\), denotes the \(n\times m\) matrix given by \[A^{T} = \left[ a _{ij}\right] ^{T}= \left[ a_{ji} \right]\nonumber \] The \(\left( i, j \right)\)-entry of \(A\) becomes the \(\left( j,i \right)\)-entry of \(A^T\).
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