Exercises - Mathematics for Data Science

Exercises for Winter Semester 2025/2026.
The numbers refer to the chapter-end exercises in Humpherys/Jarvis/Evans Volume 1.
Return to class web page

Week 7

Due on Monday, December 1

  1. Exercise 4.29
  2. Exercise 4.32
  3. Exercise 4.36
  4. Exercise 5.2
  5. Exercise 5.11

For discussion Thursday, November 27

  1. Exercise 4.28
  2. Exercise 4.30
  3. Exercise 4.31
  4. Exercise 5.1
  5. Exercise 5.9

Week 6

Due on Monday, November 24

  1. Use Schur’s lemma to show that a skew-Hermitian matrix is orthonormally diagonalizable and its eigenvalues are purely imaginary.
  2. Exercise 4.13
  3. Exercise 4.16
  4. Exercise 4.25
  5. Exercise 4.27

For discussion Thursday, November 20

  1. Exercise 4.1
  2. Exercise 4.2
  3. Exercise 4.14
  4. Exercise 4.17
  5. Exercise 4.22

Week 5

Due on Monday, November 17

  1. Prove equation (3.2.7) in Theorem 3.5.20
  2. Exercise 3.17
  3. Exercise 3.29
  4. Exercise 3.37 (You may take the inner product over the interval [-1,1]. In that case, you can directly refer to Example 3.3.3 for a suitable orthonormal basis. If you work on [0,1] as stated in the exercise, you need to compute an orthonormal basis first, or find it in the literature.)
  5. Exercise 3.47

For discussion Thursday, November 13

  1. Exercise 3.16
  2. Exercise 3.26
  3. Exercise 3.40
  4. Exercise 3.44
  5. Exercise 4.46

Week 4

Due on Monday, November 10

  1. Exercise 2.51
  2. Exercise 3.2
  3. Exercise 3.8
  4. Exercise 3.11
  5. Exercise 3.15

For discussion on Thursday, November 6

  1. Exercise 2.50
  2. Exercise 2.52
  3. Exercise 3.1
  4. Exercise 3.5
  5. Exercise 3.10

Week 3

Due on Monday, November 3

  1. Exercise 2.19
  2. Exercise 2.20
  3. Exercise 2.25
  4. Exercise 2.38
  5. Exercise 2.40

For discussion on Thursday, October 30 - do not turn in

  1. Exercise 2.13
  2. Exercise 2.14
  3. Exercise 2.21
  4. Exercise 2.23
  5. Exercise 2.30

Week 2

Due on Monday, October 27

  1. Exercise 1.9
  2. Exercise 1.11
  3. Exercise 1.12
  4. Exercise 1.14
  5. Exercise 1.23

For discussion on Thursday, October 23 - do not turn in

  1. Exercise 2.1
  2. Exercise 2.2
  3. Exercise 2.3

Week 1

For discussion on Thursday, October 16 - do not turn in

  1. Exercise 1.1
  2. Exercise 1.3
  3. Exercise 1.4
  4. Exercise 1.5
  5. Exercise 1.6
  6. Exercise 1.7 and 1.8
  7. Excercise 1.15 and 1.16
  8. Work through the proof of Theorem 1.3.7. Can you explain the overall logic, can you explain the details of each step?