Matrix Transposition Operation

From GM-RKB
(Redirected from matrix transposition)
Jump to navigation Jump to search

A Matrix Transposition Operation is a unary matrix operation that converts an m×n matrix into an n×m matrix (the matrix transpose) by sequentially swapping matrix rows with matrix columns.



References

2014

  • (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/Transpose Retrieved:2014-5-18.
    • In linear algebra, the transpose of a matrix A is another matrix AT (also written A′, Atr,tA or At) created by any one of the following equivalent actions:
      • reflect A over its main diagonal (which runs from top-left to bottom-right) to obtain AT
      • write the rows of A as the columns of AT
      • write the columns of A as the rows of AT
    • Formally, the i th row, j th column element of AT is the j th row, i th column element of A:  :[math]\displaystyle{ [\mathbf{A}^\mathrm{T}]_{ij} = [\mathbf{A}]_{ji} }[/math]

      If A is an matrix then AT is an matrix.

      The transpose of a matrix was introduced in 1858 by the British mathematician Arthur Cayley. [1]

  1. 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.