Eigenvalues as Optimization

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Linear Algebra › Eigenvalues as Optimization

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1

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

False

CORRECT

True

0

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 .

2

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

The largest eigenvalue

CORRECT

The smallest eigenvalue

0

The eigenvalue with the greatest multiplicity

0

The second largest eigenvalue

0

None of the other answers

0

Explanation

This is the statement of the Constrained Extremum Theorem. Likewise, the minimum value of the quadratic form corresponds to the smallest eigenvalue of .

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