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Example Question #71 : Matrix Calculus
True or False, the Constrained Extremum Theorem only applies to skew-symmetric matrices.
Possible Answers:
False
True
Correct answer:
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 #1 : Eigenvalues As Optimization
The maximum value of a quadratic form ( is an symmetric matrix, ) corresponds to which eigenvalue of ?
Possible Answers:
The eigenvalue with the greatest multiplicity
None of the other answers
The largest eigenvalue
The second largest eigenvalue
The smallest eigenvalue
Correct answer:
The largest eigenvalue
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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