Transpose

This article is about the transpose of matrices and linear operators. For other uses, see Transposition (disambiguation).
The transpose AT 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, 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 (among other notations).[1]

The transpose of a matrix was introduced in 1858 by the British mathematician Arthur Cayley.[2] In the case of a logical matrix representing a binary relation R, the transpose corresponds to the converse relation RT.

  1. ^ Nykamp, Duane. "The transpose of a matrix". Math Insight. Retrieved September 8, 2020.
  2. ^ Arthur Cayley (1858) "A memoir on the theory of matrices", Philosophical Transactions of the Royal Society of London, 148 : 17–37. The transpose (or "transposition") is defined on page 31.