Transpose ○◂｜Definition｜1st｜20251119205401-00-⌔

Transpose - Wikipedia

Transpose

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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).¹

The transpose of a matrix was introduced in 1858 by the British mathematician Arthur Cayley.²

Printed 2026-06-28.

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Footnotes

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. ↩