On the Space of Matrices fi (A)

Year 1974, Volume: 23 , - , 01.01.1974

E. Kaya

https://doi.org/10.1501/commua1-2_0000000014

Abstract

In this article A will be a fixed n x n m atrix andxF (x) its m inim al polynom ial of degree m. The set of m atrices fj. (A), where f* (A) is a polynom ial, is an m-dimensional subspace of th e n 2 -dim ensional space of ali n x n m atrices [1]. The set of m atrices r^(A), where
(fi ( x ) ,T (x)) - 1 and ff (x) = r. (x) (m o d Y (x) ) is a com m utative group under m atrix m ultiplication w hich is isom orphic to the group of polynom ials r^ (x) under m ultiplication modT* (x). W e also characterize properties of the m atrices f^ (A) in term s of properties of the polynom ials T (x).

Keywords

space, matrices, mathematics

References

• Communications, Series A2-A3: Physical Sciences and Engineering