Vipul: Created page with "{{square matrix property}} ==Definition== ===Verbal definition=== A square matrix is termed a '''skew-symmetric matrix''' if is negative equals its matrix transpose..."

2014-05-01T05:39:07Z

Created page with "{{square matrix property}} ==Definition== ===Verbal definition=== A square matrix is termed a '''skew-symmetric matrix''' if is negative equals its matrix transpose..."

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{{square matrix property}}

==Definition==

===Verbal definition===

A [[square matrix]] is termed a '''skew-symmetric matrix''' if is negative equals its [[matrix transpose]]. In symbols, a matrix <math>A</math> is termed skew-symmetric if <math>-A = A^T</math>.

===Algebraic definition===

Suppose <math>n</math> is a positive integer and <math>A = (a_{ij})_{1 \le i \le n, 1 \le j \le n}</math> is a <math>n \times n</math> matrix. We say that <math>A</math> is skew=symmetric if the following holds:

<math>a_{ij} = -a_{ji} \ \forall \ i, j \in \{ 1,2,\dots,n \}</math>

Because the equality condition is symmetric in <math>i,j</math>, it suffices to check it for <math>i < j</math>, so the above definition if equivalent to:

<math>a_{ij} = a_{ji} \ \forall \ i \le j \in \{ 1,2,\dots,n \}</math>

Note that it is important to include the condition on the diagonal elements, and that this condition forces the diagonal elements to all equal zero.

Skew-symmetric matrix - Revision history

Vipul: Created page with "{{square matrix property}} ==Definition== ===Verbal definition=== A square matrix is termed a '''skew-symmetric matrix''' if is negative equals its matrix transpose..."