# 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**A**^{T}(also written**A**′,**A**^{tr},^{t}**A**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}

- reflect
- 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.

^{[1]}

- In linear algebra, the

- ↑ 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.