Transpose of a Matrix

Transpose of a Matrix

Associated with each given matrix there exists another matrix called its Transpose . The

transpose of a given matrix A is formed by interchanging its row and columns and is

denoted by $A^{'} or A^{t}$ . If

$A = \begin{bmatrix} 1 & 2 & -3\\ 4& 0 & 3\\ 7& 6 & 1 \end{bmatrix} , then\ A^{t} = \begin{bmatrix} 1 & 4 & 7\\ 2 & 0 & 6\\ -3 & 3 & 1 \end{bmatrix}$
In general, If $A = [a_{ij}]$ is an " m x n " matrix, then the transpose $A^'$ of $A$ is the " n x m"
matrix ; and, $(a_{ij})th$ element of $A = (a_{ij})th$ element of $A^'$ .

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Transpose of a Matrix

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