[Axiom-mail] Inverting a matrix over a modular integer ring
From:
Alasdair McAndrew
Subject:
[Axiom-mail] Inverting a matrix over a modular integer ring
Date:
Sun, 27 May 2007 19:53:05 +1000
Suppose I create the matrix
M:=matrix([[random()$PF(19) for i in 1..3] for j in 1..3])
Assuming the determinant is non-zero, then I can invert the matrix in the finite field PF(19). But suppose I enter
N:=matrix([[random()$ZMOD(20) for i in 1..3] for j in 1..3])
If the determinant is relatively prime to 20, then the inverse of N exists over the ring ZMOD(20). But division is not defined in ZMOD - so how do I invert N?