Normal Forms for Orthogonal Similarity Classes of Skew-symmetric Matrices

@inproceedings{RIETSCH2006NormalFF,
title={Normal Forms for Orthogonal Similarity Classes of Skew-symmetric Matrices},
author={KONSTANZE RIETSCH and Kaiming Zhao},
year={2006}
}

Let F be an algebraically closed field of characteristic different from 2. Define the orthogonal group, On(F), as the group of n by n matrices X over F such that XX ′ = In, where X ′ is the transpose of X and In the identity matrix. We show that every nonsingular n by n skew-symmetric matrix over F is orthogonally similar to a bidiagonal skew-symmetric matrix. In the singular case one has to allow some 4-diagonal blocks as well. If further the characteristic is 0, we construct the normal form… CONTINUE READING