Transpose of a Matrix

Transpose of a Matrix

Matrix M\(^{\textrm{T}}\) obtained by interchanging the rows and columns of a given matrix M such that each element \(a_{ij}\) of M becomes the element \(a_{ji}\) of M\(^{\textrm{T}}\).


The transpose of matrix A below is matrix B.

A = \(\begin{pmatrix} –3 & 6 & 7\\4 & –8 & 5\end{pmatrix}\)

B = \(\begin{pmatrix} –3 & 4\\6 & –8\\7 & 5\end{pmatrix}\)

Therefore, the matrices A and B are compatible.

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