advanced-linear-algebra

Constrained quadratic optimization and the generalized eigenvalue problem

taught

Optimizing $x^{\mathsf T}Ax$ subject to a second quadratic constraint $x^{\mathsf T}Bx=1$ reduces to the generalized eigenvalue problem $Ax=\lambda Bx$, the natural two-matrix generalization of the Rayleigh quotient.

Taught in

Constrained quadratic optimization and the generalized eigenvalue problem
Advanced Linear Algebra

Requires

the-courant-fischer-min-max-theorem required
four-tests-for-definiteness required

Required by

Nothing in the catalog needs this yet.

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