Transpose Operation

A Transpose Operation is a Linear Algebra Operator that flips a matrix or over its diagonal.

• Example(s):
  • Matrix Transpose,
  • Tensor Transpose.
  • …
• Counter-Example(s):
  • Conjugate Transpose,
  • Binary Operation,
  • Unary Operation,
  • Symmetry Operation,
• See: Arthur Cayley, Transpose of a Linear Map, Linear Algebra, Matrix (Mathematics).

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References

2020a

• (Wikipedia, 2020) ⇒ https://en.wikipedia.org/wiki/Transpose Retrieved:2020-8-9.
  • In linear algebra, the transpose of a matrix is an operator which flips a matrix over its diagonal;

    that is, it switches the row and column indices of the matrix A by producing another matrix, often denoted by A^T (among other notations).

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

2020b

• (Weisstein, 2020b) ⇒ Weisstein, Eric W. "Transpose". From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Transpose.html
  • QUOTE: A transpose of a doubly indexed object is the object obtained by replacing all elements $a_{ij}$ with $a_{ji}$. For a second-tensor rank tensor $a_{ij}$, the tensor transpose is simply $a_{ji}$. The matrix transpose, most commonly written $A^{T}$, is the matrix obtained by exchanging $A$'s rows and columns, and satisfies the identity
    $\left(A^{T}\right)^{-1}=\left(A^{-1}\right)^{T}$.

    Unfortunately, several other notations are commonly used, as summarized in the following table. The notation $A^{T}$ is used in this work.

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