Some results about the Equiangular Algorithm

TL;DR

This paper explores properties, inverse and eigenvalue problems, and canonical forms of equiangular matrices generated by the Equiangular Algorithm, which constructs equiangular vectors with a specified angle in a real inner product space.

Contribution

It introduces new properties and canonical forms of equiangular matrices, and studies their inverse and eigenvalue problems, expanding understanding of these matrices.

Findings

Properties of equiangular matrices are characterized.

Canonical forms of matrices based on equiangular matrices are derived.

Inverse and eigenvalue problems for these matrices are analyzed.

Abstract

Equiangular Algorithm generates a set of equiangular normalized vectors with given angle {\theta} using a set of linearly independence vectors in a real inner product space, which span the same subspaces. The outcome of EA on column vectors of a matrix A provides a matrix decomposition A = SR, where S is called Equiangular Matrix which has equiangular column vectors. In this paper we discuss some properties of equiangular matrices. The inverse and eigenvalue problems of these matrices are studied. Also we derive some canonical forms of some matrices based on equiangular ones.