Transpose

In linear algebra, the transpose of a matrix A is another matrix AT (also written A′, Atr or At) created by any one of the following equivalent actions:

  • reflect A over its main diagonal (which runs 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 ith row, jth column element of AT is the jth row, ith column element of A:

If A is an m × n matrix then AT is an n × m matrix.

Read more about Transpose:  Examples, Properties, Special Transpose Matrices, Transpose of Linear Maps, Implementation of Matrix Transposition On Computers

Famous quotes containing the word transpose:

    “We have to transpose ourselves into this impressionability of mind, into this sensitivity to tears and spiritual repentance, into this susceptibility, before we can judge how colorful and intensive life was then.”
    —Johan Huizinga (1872–1945)