Machine Learning Foundations Quiz 2: 6 August 2023 (May 2023 term)

Select all that apply.

1. A

   The eigenvalues of a Hermitian matrix are always real.

2. B

   The diagonal elements of a Hermitian matrix are always real.

3. C

   All symmetric matrices are Hermitian.

4. D

   All Hermitian matrices are symmetric.

Select all that apply.

1. A

   A matrix that is both unitary and Hermitian must be a diagonal matrix.

2. B

   A matrix that is both unitary and Hermitian need not be a diagonal matrix.

3. C

   If matrix A is unitary, then A* is unitary.

4. D

   If matrix A is unitary then, A* may not be unitary.

Select all that apply.

1. A

   If a function is positive semidefinite, then it only has a global minimum.

2. B

   If a function is positive semidefinite, then it has both global minimum and global maximum.

3. C

   If a function is negative semidefinite, then it only has a global maximum.

4. D

   If a function is negative semidefinite, then it has both global minimum and global maximum.