Coefficients of Higher Powers of a Matrix: Companion Matrix

EasyChair Preprint 6678

Abstract

For  any  NxN  square  matrix  X,  higher powers  of  it,  can  be  expressed  in  terms  of  { I, X, ....., X power N-1 }.  The  coefficients  of   them  are   proved  to  be  expressible  in  terms  of  companion  matrix  of  X.

Keyphrases: Cayley-Hamilton theorem, Companion matrix, Higher Powers of Matrix, recursive computation

@booklet{EasyChair:6678,
  author    = {Rama Garimella and Basa Chandraneil and Rumyantsev Alexander},
  title     = {Coefficients  of  Higher  Powers  of  a  Matrix:  Companion  Matrix},
  howpublished = {EasyChair Preprint 6678},
  year      = {EasyChair, 2021}}