On the jordan form of the tensor product over fields of prime characteristic |
| |
Authors: | C W Norman |
| |
Institution: |
a Department of Mathematics, Royal Holloway and Bedford New college, Egham, Surrey, United Kingdom |
| |
Abstract: | Let A, B denote the companion matrices of the polynomials xm,xn over a field F of prime order p and let λ,μ be non-zero elements of an extension field K of F. The Jordan form of the tensor product (λI + A)?(μI + B) of invertible Jordan matrices over K is determined via an equivalent study of the nilpotent tranformation S of m × n matrices X over F where(X)S = A TX + XB. Using module-theoretic concepts a Jordan basis for S is specified recursively in terms of the representations of m and n in the scale of p, and reduction formulae for the elementary divisors of S are established. |
| |
Keywords: | |
本文献已被 InformaWorld 等数据库收录! |
|