A be an n n matrix with eigenvalues 1 , , k , and B an m m matrix with eigenvalues 1 , , l Show that the (m n) (m n) block diagonal matrix has eigenvalues 1 , , k , 1 , , l and no others How are the eigenvectors related D A

Question: A be an n n matrix with eigenvalues 1 , . . . , k , and B an m m

A be an n × n matrix with eigenvalues λ₁, . . . , λ_k, and B an m × m matrix with eigenvalues μ₁, . . . , μ_l. Show that the (m + n) × (m + n) block diagonal matrix has eigenvalues λ₁, . . . , λ_k, μ₁, . . . , μ_l and no others. How are the eigenvectors related?

D= A

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