Matrix diagonalisieren • Diagonalmatrix, Diagonalisierbarkeit

Answered: Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D. To save time, the eigenvalues are -6 and 3. - 2 - 2 - 4 A = -2 - 5 -… | bartleby

Suppose that a matrix A has characteristic polynomial p(x) = x^4 - 1. Use an argument involving diagonalization to show that A^4 = A. As part of your answer, explain why A is diagonalizable over C (Do not use the Cayley-Hamilton Theorem if you know it).