Question: Some one help? (1) Suppose A is an n x n diagonalizable real matrix. Show that rank(A - A/) = rank(A - XI) for every

Some one help?

(1) Suppose A is an n x n diagonalizable real matrix. Show that rank(A - A/) = rank(A - XI) for every JER. (2) Let A be an n x n real matrix with n real eigenvalues (counting algebraic multiplicities). Suppose that rank(A -XI) = rank(A- XI)2 for every A E R. Prove that A is diagonalizable. (Hint: Jordan normal form. )

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