Suppose matrix has the set of elementary divisors given by a

Suppose matrix has the set of elementary divisors given by:

a) the size of A (i.e. if A is n x n, what is n?)

b) the invariant factors of A

c) the determinantal divisors of A

d) a Jordan canonical form for A

A -1, A 1, (A 1)3, (A 1)4, (A 2)2, (A 2)2, (A-2) 4, A-3, (A 3)

Solution

a) n=4, the matrix A is a 4x4 matrix because the highest power of elementory divisors is 4.