Semi-involutory matrices and signed self-inverse

In this paper three new classes of matrices that have a computationally simple inverse are studied. Specifically, semi-involutory matrices are characterized for small orders and many interesting results are provided. Semi-involutory matrices can be thought of as a generalization of involutory matrices. In addition, signed semi-involutory matrices are studied and a natural generalization is introduced. (c) 2021 Elsevier Inc. All rights reserved.