Transpose

This article is about the transpose of matrices and linear operators. For other uses, see Transposition (disambiguation).

The transpose A^T of a matrix A can be obtained by reflecting the elements along its main diagonal. Repeating the process on the transposed matrix returns the elements to their original position.

In linear algebra, transposition is an operation that flips a matrix over its diagonal; that is, transposition switches the row and column indices of the matrix A to produce another matrix, called the transpose of A and often denoted A^T (among other notations).

The transpose of a matrix was introduced in 1858 by the British mathematician Arthur Cayley.