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Example Questions
Example Question #71 : Matrix Calculus
True or False, the Constrained Extremum Theorem only applies to skew-symmetric matrices.
Possible Answers:
True
False
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 second largest eigenvalue
The largest eigenvalue
The eigenvalue with the greatest multiplicity
The smallest eigenvalue
None of the other answers
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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