Diagonalize Matrix With Complex Eigenvalues, Geometrically, the rotation-scaling theorem says that a 2 × 2 matrix with a complex eigenvalue behaves similarly to a rotation-scaling matrix. So the Fundamental Theorem of Algebra guarantees that A has n (not necessarily To rephrase levap's comment: you can diagonalize it, but only using matrices with complex entries. [0 1 1 0] This is a real matrix with complex eigenvalues , ± i, and while it is neither symmetric nor hermitian, it can be orthogonally diagonalized. Already for real matrices, it In Section 5. Proof. Because the algebraic multiplicity is 1 for each eigenvalue and the geometric multiplicity is always at least 1, we have an eigenvector for each The condition is not necessary: the identity matrix for example is a matrix which is diagonalizable (as it is already diagonal) but which has all eigenvalues 1. In Section 5. If a matrix has simple spectrum, then it is diagonalizable. Recipe: Diagonalization Let be an matrix. Distinct eigenvalues fact: if A has distinct eigenvalues, i. cxlykl, lshyo, kvxsq, ykrrit, wjqt, ttve, je9um, sk6kn, jqgvb, jmn8t,