Given the following information about a 4 \times 2 matrix A: - The characteristic polynomial of A^T A is (\lambda - 48)(\lambda - 12). - Eigenvectors of A^T A corresponding to eigenvalues \lambda = 48, \lambda = 12 are q_1 = \begin{pmatrix} 1/\sqrt{2} \ 1/\sqrt{2} \end{pmatrix} and q_2 = \begin{pmatrix} 1/\sqrt{2} \ -1/\sqrt{2} \end{pmatrix}, respectively. - Aq_1 = \begin{pmatrix} 4/\sqrt{2} \ -8/\sqrt{2} \ 0 \ 4/\sqrt{2} \end{pmatrix}, Aq_2 = \begin{pmatrix} -2/\sqrt{2} \ 0 \ 4/\sqrt{2} \ 2/\sqrt{2} \end{pmatrix} What is the matrix A?

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Anwer the given subquestions. Figure from the original question paper

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Anwer the given subquestions. Figure from the original question paper

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May 2023 term · Machine Learning Foundations · BSCS2004

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

The IIT Madras BS Machine Learning Foundations (MLF) Quiz 2 paper sat on 6 Aug 2023, in the May 2023 term: 13 questions for 40 marks in 120 minutes. Every question is below with its answer. Take it as a timed mock test to be marked, or read it through first.

Questions: 13
Marks: 40
Duration: 120 min
MSQ: 3
Numerical: 5
MCQ: 5

Take as mock test Practise with answers

Updated 25 Sept 2026

Official paper: IIT M FOUNDATION AN2 EXAM QPF2 06 Aug 2023 · No negative marking.

Question 1

+3 marksOne or more correct options

Which among the following is/are true for a Hermitian matrix?

Select all that apply.

A
The eigenvalues of a Hermitian matrix are always real.
B
The diagonal elements of a Hermitian matrix are always real.
C
All symmetric matrices are Hermitian.
D
All Hermitian matrices are symmetric.

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Correct answers

A
The eigenvalues of a Hermitian matrix are always real.
B
The diagonal elements of a Hermitian matrix are always real.

Question 1 on its own page

Question 2

+3 marksOne or more correct options

Which of the following options are true?

Select all that apply.

A
A matrix that is both unitary and Hermitian must be a diagonal matrix.
B
A matrix that is both unitary and Hermitian need not be a diagonal matrix.
C
If matrix A is unitary, then A* is unitary.
D
If matrix A is unitary then, A* may not be unitary.

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Correct answers

B
A matrix that is both unitary and Hermitian need not be a diagonal matrix.
C
If matrix A is unitary, then A* is unitary.

Question 2 on its own page

Question 3

+3 marksOne or more correct options

Which among the following statements is/are true?

Select all that apply.

A
If a function is positive semidefinite, then it only has a global minimum.
B
If a function is positive semidefinite, then it has both global minimum and global maximum.
C
If a function is negative semidefinite, then it only has a global maximum.
D
If a function is negative semidefinite, then it has both global minimum and global maximum.

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Correct answers

A
If a function is positive semidefinite, then it only has a global minimum.
C
If a function is negative semidefinite, then it only has a global maximum.

Question 3 on its own page

Question 4

+3 marksNumerical answer

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Correct answer: 3

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Question 5

+3 marksNumerical answer

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Correct answer: 4

Question 5 on its own page

Question 6

+3 marksOne correct option

Which among the following functions are positive definite?

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Correct answer

Question 6 on its own page

Question 7

+4 marksOne correct option

Given the following information about a $4 \times 2$ matrix $A$ :

The characteristic polynomial of $A^T A$ is $(\lambda - 48)(\lambda - 12)$ .
Eigenvectors of $A^T A$ corresponding to eigenvalues $\lambda = 48$ , $\lambda = 12$ are $q_1 = \begin{pmatrix} 1/\sqrt{2} \\ 1/\sqrt{2} \end{pmatrix}$ and $q_2 = \begin{pmatrix} 1/\sqrt{2} \\ -1/\sqrt{2} \end{pmatrix}$ , respectively.
$Aq_1 = \begin{pmatrix} 4/\sqrt{2} \\ -8/\sqrt{2} \\ 0 \\ 4/\sqrt{2} \end{pmatrix}$ , $Aq_2 = \begin{pmatrix} -2/\sqrt{2} \\ 0 \\ 4/\sqrt{2} \\ 2/\sqrt{2} \end{pmatrix}$