Linear algebra (Osnabrück 2024-2025)/Part I/Enumeration of 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