Eigenvalues as Optimization - Linear Algebra
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Question
True or False, the Constrained Extremum Theorem only applies to skew-symmetric matrices.
True or False, the Constrained Extremum Theorem only applies to skew-symmetric matrices.
Answer
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 
.
It only applies to symmetric matrices, not skew-symmetric ones. The Constrained Extremum Theorem concerns the maximum and minimum values of the quadratic form
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Question
The maximum value of a quadratic form 
(
is an 
symmetric matrix, 
) corresponds to which eigenvalue of 
?
The maximum value of a quadratic form
Answer
This is the statement of the Constrained Extremum Theorem. Likewise, the minimum value of the quadratic form corresponds to the smallest eigenvalue of 
.
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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