Module: Spectral Decomposition

Learning Outcomes

Spectral Decomposition

• You know how to compute eigenvalues and eigenvectors of a matrix
• The set of all eigenvectors with the same eigenvalue (plus the all-0 vector) is a linear space, the eigenspace
• Algebraic multiplicity (AM) and Geometric multiplicities (GM) of eigenvalues * Similar matrices
• Specialization to symmetric matrices: real eigenvalues, AM=GM for all eigenvalues, distinct eigenvalues have orthogonal eigenspaces
• Symmetric matrices: Orthonormal basis using eigenvectors

Readings

Experiential Learning