determine similarity of matrices
Issimilar(A, B, 'P')
(optional) assigned a transformation matrix
The function Issimilar(A, B) is a placeholder for the boolean valued function that returns true if A is similar to B and false otherwise. It is used in conjunction with either mod or evala.
If called in the form Issimilar(A, B,'P'), then P will be assigned a transformation matrix such that A=inverse⁡P⁢B⁢P.
The call Issimilar(A, B) mod p determines if A is similar to B modulo p which is a prime integer. The entries of A and B must have rational coefficients or coefficients from an algebraic extension of the integers modular p.
The call evala(Issimilar(A, B)) determines if A is similar to B where the entries of A and B are algebraic numbers (or functions) defined by RootOfs.
A ≔ Matrix⁡1,2,3,4,5,6,7,8,9
p ≔ 11
cA ≔ CharacteristicPolynomial⁡A,xmodp
B ≔ CompanionMatrix⁡cA,x
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