Matrix Transpose

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 Aᵀ

The matrix transpose is the matrix obtained by replacing all elements $a_{ij}$ with $a_{ji}$ or, which is the same, by exchanging A's rows and columns, or flipping A over its diagonal. The matrix transpose is often written as $A^T$