advanced-linear-algebra

Conditioning and the perturbation of eigenvalues

taught

Weyl's inequality bounds eigenvalue drift tightly for a symmetric matrix, but a non-normal matrix's eigenvalues can be dramatically more sensitive to a tiny perturbation -- conditioning depends on more than just the matrix's own eigenvalues.

Taught in

Conditioning and the perturbation of eigenvalues
Advanced Linear Algebra

Requires

the-neumann-series-and-the-resolvent required
eigenvalue-interlacing-and-weyls-inequality required

Required by

Approximate eigenvectors and why the spectrum can be unstable required

Local knowledge map

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