Editing Transpose (section)

{{Short description|Matrix operation which flips a matrix over its diagonal}}
{{about|the transpose of matrices and [[Transpose of a linear map|linear operators]]||Transposition (disambiguation)}}
[[File:Matrix transpose.gif|thumb|200px|right|The transpose '''A'''<sup>T</sup> 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 (mathematics)|matrix]] is an operator which flips a matrix over its diagonal;
that is, it switches the row and column indices of the matrix {{math|'''A'''}} by producing another matrix, often denoted by {{math|'''A'''<sup>T</sup>}} (among other notations).<ref>{{Cite web|last=Nykamp|first=Duane|title=The transpose of a matrix|url=https://mathinsight.org/matrix_transpose|access-date=September 8, 2020|website=Math Insight}}</ref> 

The transpose of a matrix was introduced in 1858 by the British mathematician [[Arthur Cayley]].<ref>Arthur Cayley (1858) [https://books.google.com/books?id=flFFAAAAcAAJ&pg=PA31 "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.</ref>