Linear algebra (Osnabrück 2024-2025)/Part I/Exercise sheets

Information

• Content

Lectures

• 1 - Sets

• 2 - Mappings

• 3 - Groups and fields

• 4 - Linear systems

• 5 - Solving linear systems

• 6 - Vector spaces

• 7 - Linear independence

• 8 - Dimension

• 9 - Base change

• 10 - Linear mappings

• 11 - Subspaces under linear mappings

• 12 - Invertible matrices

• 13 - Projections

• 14 - Linear forms

• 15 - Subspaces and dual space

• 16 - Determinants

• 17 - Universal property

• 18 - Permutations

• 19 - Polynomials

• 20 - Interpolation

• 21 - Eigenspaces

• 22 - Relations among eigenspaces

• 23 - Characteristic polynomial

• 24 - Theorem of Cayley-Hamilton

• 25 - Trigonalizability

• 26 - Lemma of Bezout

• 27 - Nilpotent mappings

• 28 - Jordan normal form

• 29 - Affine spaces

• 30 - Affine generating systems

Exercise sheets

• Exercise sheet 1

• Exercise sheet 2

• Exercise sheet 3

• Exercise sheet 4

• Exercise sheet 5

• Exercise sheet 6

• Exercise sheet 7

• Exercise sheet 8

• Exercise sheet 9

• Exercise sheet 10

• Exercise sheet 11

• Exercise sheet 12

• Exercise sheet 13

• Exercise sheet 14

• Exercise sheet 15

• Exercise sheet 16

• Exercise sheet 17

• Exercise sheet 18

• Exercise sheet 19

• Exercise sheet 20

• Exercise sheet 21

• Exercise sheet 22

• Exercise sheet 23

• Exercise sheet 24

• Exercise sheet 25

• Exercise sheet 26

• Exercise sheet 27

• Exercise sheet 28

• Exercise sheet 29

• Exercise sheet 30

Further material

• List of definitions
• Important theorems

Forum

Literature

Links

• Exercise sheet 1

• Exercise sheet 2

• Exercise sheet 3

• Exercise sheet 4

• Exercise sheet 5

• Exercise sheet 6

• Exercise sheet 7

• Exercise sheet 8

• Exercise sheet 9

• Exercise sheet 10

• Exercise sheet 11

• Exercise sheet 12

• Exercise sheet 13

• Exercise sheet 14

• Exercise sheet 15

• Exercise sheet 16

• Exercise sheet 17

• Exercise sheet 18

• Exercise sheet 19

• Exercise sheet 20

• Exercise sheet 21

• Exercise sheet 22

• Exercise sheet 23

• Exercise sheet 24

• Exercise sheet 25

• Exercise sheet 26

• Exercise sheet 27

• Exercise sheet 28

• Exercise sheet 29

• Exercise sheet 30