Matrix Transposition Operation
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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):
- See: Real Matrix.
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]
- 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:
- ↑ 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.