Linear Algebra : Eigenvalues as Optimization

Example Questions

Example Question #1 : Eigenvalues As Optimization

True or False, the Constrained Extremum Theorem only applies to skew-symmetric matrices.

False

True

False

Explanation:

It only applies to symmetric matrices, not skew-symmetric ones. The Constrained Extremum Theorem concerns the maximum and minimum values of the quadratic form  when .

Example Question #2 : Eigenvalues As Optimization

The maximum value of a quadratic form  ( is an  symmetric matrix, ) corresponds to which eigenvalue of ?

The smallest eigenvalue

The largest eigenvalue

The eigenvalue with the greatest multiplicity

The second largest eigenvalue