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Key Issues: Lecture IV Real symmetric matrices and canonical forms Fall 2020 Prof.Jiang@ECE NYU 159 Symmetric Matrices Recall that a symmetric matrix A  aij  satisfies: aijaji, 1i,jn. It is a real symmetric matrix if, additionally, all aij ‘ s are real. Notation : T nn AA,A . Fall 2020 Prof.Jiang@ECE NYU 160 Fact

Lecture VII • The Jordan Canonical Form • Examples and Applications Fall 2020 Prof.Jiang@ECE NYU 295 Review of Canonical Forms  If A is an n  n matrix with distinct eigenvalues, then there exists a nonsingular matrix P s.t. P1 AP  diag i .  If A is Hermitian (possibly having repeated eigenvalues),

Key issues: Lecture III • Eigenvalues, eigenvectors and the characteristic polynomial of a square matrix • Similarity Fall 2020 Prof.Jiang@ECE NYU 115 Definition: Eigenvalue and Eigenvector Given a square n  n matrix A, the set of eigenvalues    are such that the characteristic equation Ac  c , or equivalently I 