### All Linear Algebra Resources

## Example Questions

### Example Question #1 : Eigenvalues As Optimization

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 #2 : Eigenvalues As Optimization

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

**Possible Answers:**

The smallest eigenvalue

None of the other answers

The largest eigenvalue

The eigenvalue with the greatest multiplicity

The second largest 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 .

Mahdi

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