arXiv subjects

Azim Rivaz

Publications and source records attributed to Azim Rivaz.

2 recordsLinked to original sources

arXiv2016

Some results about the Equiangular Algorithm

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.

math.NA↗

arXiv2014

An introduction to the Equiangular algorithm

In this paper a generalization of the Gram-Schmidt Algorithm is presented. Actually we provide an algorithm to construct a set of equiangular vectors with a given angle $\theta\in(0,\arccos(\frac{-1}{n-1}))$ using a set of input independent vectors in $\mathbb{R}^n$. Therefore a usual type of matrix decomposition is derived. Then we discuss some properties of matrices derived from the new algorithm. The inverse and eigenvalue problems of these matrices if there exist are studied. Also, we derive some canonical forms based on the algorithm.

math.NA↗