Linear algebra (Osnabrück 2024-2025)/Part II

In preparation

Information

• Content

Lectures

• 31 - Vector spaces with inner product

• 32 - Orthogonality

• 33 - Isometries I

• 34 - Isometries II

• 35 - Set distances

• 36 - Intercept theorems

• 37 - Triangle geometry

• 38 - Bilinear forms

• 39 - Types of bilinear forms

• 40 - Minkowski-spaces

• 41 - Adjoint endomorphism

• 42 - Normal endomorphism

• 43 - Quadratic forms

• 44 - Group homomorphisms

• 45 - Equivalence relations

• 46 - Residue class formation

• 47 - Homomorphy theorems

• 48 - Residue class spaces

• 49 - Orientations

• 50 - Finite symmetry groups I

• 51 - Finite symmetry groups II

• 52 - Equivalent norms

• 53 - Convergence of matrix powers

• 54 - Stochastic matrices

• 55 - Tensor product I

• 56 - Tensor product II

• 57 - Wedge product I

• 58 - Wedge product II

Exercise sheets

• Exercise sheet 31

• Exercise sheet 32

• Exercise sheet 33

• Exercise sheet 34

• Exercise sheet 35

• Exercise sheet 36

• Exercise sheet 37

• Exercise sheet 38

• Exercise sheet 39

• Exercise sheet 40

• Exercise sheet 41

• Exercise sheet 42

• Exercise sheet 43

• Exercise sheet 44

• Exercise sheet 45

• Exercise sheet 46

• Exercise sheet 47

• Exercise sheet 48

• Exercise sheet 49

• Exercise sheet 50

• Exercise sheet 51

• Exercise sheet 52

• Exercise sheet 53

• Exercise sheet 54

• Exercise sheet 55

• Exercise sheet 56

• Exercise sheet 57

• Exercise sheet 58

Further material

• List of definitions
• Important theorems

Forum

Literature

Links

The zero set of a quadratic polynomial in three variables is called a quadric. These quadrics can be classified with methods from linear algebra.

Linear algebra is a fundamental course in mathematics. It deals with "linear structures“: linear systems of equations, vectors and their representation, bases and base change, linear mappings and matrices, determinants, eigenvalues and eigenvectors, optimal descriptions of linear mappings, affine mappings, normed vector spaces, lengths and angles, analytic geometry, isometries and symmetries, bilinear forms, more general algebraic structures like equivalence relations, groups, residue class construction, and multilinear algebra.