Example of Rational Canonical Form 3

Matrix Theory: We note two formulations of Rational Canonical Form. A recipe is given for combining and decomposing companion matrices using cyclic vectors.

[manishsapkal]

Please do a lecture of examples 'to find rational canonical form for given matrix'

[MathDoctorBob]

As I note, there are different ways to formulate RCF. The usual way is to separate the blocks into companion matrices associated to powers of irreducible polynomials, hence the diagonal.

Alternatively the companion matrices are arranged so that the polynomial for one block divides the polynomial of the next. In this case, one sees that, for a diagonal matrix A with distinct eigenvalues, C^n has a generating/cyclic vector under A.

[shaikhaslam]

Please sir solve 3by3 matrix example on RCF