Matrix Transposition Operation

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.

• Context:
  • …
• Counter-Example(s):
  • Matrix Inversion.
• See: Real Matrix.

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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 A^T (also written A′, A^tr,^tA or A^t) 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 A^T
    • write the rows of A as the columns of A^T
    • write the columns of A as the rows of A^T
  • Formally, the i th row, j th column element of A^T 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 A^T is an matrix.

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

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