Question

Suppose that B is a 6 × 6 matrix and that it has eigenvalues λ_1 = -1, λ_2 = 3 and λ_3 = 4. The algebraic and geometric multiplicities of λ_1 are 2 and 1, respectively. The algebraic (and hence the geometric) multiplicity of λ_2 is 1. Finally, the algebraic and geometric multiplicities of λ_3 are 3 and 2, respectively. Use this information to write down 2 distinct Jordan forms of the matrix B. State the number of possible combinations for the Jordan forms. Give reasons for your answer.

Answer 1

I'm aware this might be quite an involved question, but any guidance is much appreciated :)