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A square matrix A is antisymmetric if it is equal to the negative of its transpose: Every matrix A can be decomposed into the sum of an antisymmetric and a symmetric matrix: A = B + C = (1/2) * ( ( A - A' ) + ( A + A' ) ) Simple facts about an... See more

A square matrix A is antisymmetric if it is equal to the negative of its transpose: Every matrix A can be decomposed into the sum of an antisymmetric and a symmetric matrix: A = B + C = (1/2) * ( ( A - A' ) + ( A + A' ) ) Simple facts about an antisymmetric matrix A: * A has a zero diagonal; * A has pure imaginary eigenvalues; * A is normal, hence unitarily diagonalizable. * I - A is not singular; * The matrix ( I + A ) * Inverse ( I - A ) is orthogonal; An antisymmetric matrix is also called skew symmetric. In complex arithmetic, the corresponding object is a skew Hermitian matrix. Back to TABLE OF CONTENTS. See less