Properties

Transpose of a Matrix

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

Example

The transpose of matrix A below is matrix B. A = [latex]\begin{pmatrix} –3 & 6 & 7\\4 & –8 & 5\end{pmatrix}[/latex] B = [latex]\begin{pmatrix} –3 & 4\\6 & –8\\7 & 5\end{pmatrix}[/latex] Therefore, the matrices A and B are compatible.

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