Concept

# Skew-symmetric matrix

Summary
In mathematics, particularly in linear algebra, a skew-symmetric (or antisymmetric or antimetric) matrix is a square matrix whose transpose equals its negative. That is, it satisfies the condition In terms of the entries of the matrix, if a_{ij} denotes the entry in the i-th row and j-th column, then the skew-symmetric condition is equivalent to Example The matrix :A = \begin{bmatrix} 0 & 2 & -45 \ -2 & 0 & -4 \ 45 & 4 & 0 \end{bmatrix} is skew-symmetric because : -A = \begin{bmatrix} 0 & -2 & 45 \ 2 & 0 & 4 \ -45 & -4 & 0 \end{bmatrix} = A^\textsf{T} . Properties Throughout, we assume that all matrix entries belong to a field \mathbb{F} whose characteristic is not equal to 2. That is, we assume that 1 + 1 ≠ 0, where 1 denotes the multiplicat
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