Skew-Symmetric Matrix

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A Skew-Symmetric Matrix is a square matrix, [math]\displaystyle{ A=[a_{ij}]_{\substack{i=1\dots m\\j=1\dots n}} }[/math], whose matrix transpose is also its negative, that is when [math]\displaystyle{ a_{ij} = \begin{cases} -a_{ji} & \quad \text{if } i\#j\\ 0 & \quad \text{if } i=j\\ \end{cases} }[/math]



References

2015

  • (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/skew-symmetric_matrix Retrieved:2015-2-20.
    • In mathematics, and in particular linear algebra, a skew-symmetric' (or antisymmetric or antimetric ) matrix is a square matrix A whose transpose is also its negative; that is, it satisfies the condition If the entry in the and is aij, i.e. then the skew symmetric condition is For example, the following matrix is skew-symmetric: : [math]\displaystyle{ \begin{bmatrix} 0 & 2 & -1 \\ -2 & 0 & -4 \\ 1 & 4 & 0\end{bmatrix}. }[/math]