Sentence:  The eigenvalues of an <WSD>antisymmetric</WSD> matrix are all purely imaginary numbers, and occur as conjugate pairs, +iw and -iw. As a corollary it follows that an <WSD>antisymmetric</WSD> matrix of odd order necessarily has one eigenvalue equal to zero; <WSD>antisymmetric</WSD> matrices of odd order are singular. 
Meaning of the word marked with <WSD> tags:  Whose transpose equals its negative (i.e., "M"T = −"M");