Multilineare Algebra - FS 2012

Multilineare Algebra und ihre Anwendungen

Frühjahrssemester 2012

Vorlesungsskripte (auf Englisch)

Use at your own risk! Please let know of any mistakes or imprecisions.

1. 22. Februar (PDF) how coordinates of a vector change under change of basis - contravariance;
review of vector spaces and bases
2. 29. Februar (PDF) how matrices of linear transformations change under change of basis;
Einstein summation convention
3. 7. März (PDF) linear forms, dual vector space, dual basis;
how linear forms change under change of basis - covariance
4. 14. März (PDF) linear forms - an example with computations;
bilinear forms, tensor product of linear forms, basis for space of bilinear forms
5. 21. März (PDF) blinear forms, components and matrix w.r.t. a basis, covariance;
trilinear and k-linear forms; inner products, orthonormal basis
6. 28. März (PDF) inner products, orthonormal bases;
reciprocal basis, covariant coordinates
7. 4. April (PDF) contravariance of reciprocal basis, raising and lowering indices;
canonical identification between V and its dual given by metric
8. 18. April (PDF) (2,0)-tensors, (p,q)-tensors;
inertia tensor: angular velocity and kinetic energy
9. 25. April (PDF) inertia tensor, moment of inertia, angular momentum;
principal axes of inertia, principal moments of inertia, ellipsoid of inertia
10. 2. Mai (PDF) tensor product of arbitrary tensors, tensor product of vector spaces;
bilinear (or multilinear) functions viewed as linear functions on tensor products
11. 9. Mai (PDF) and text copies (PDF) stress tensor, principal stresses and principal directions;
hydrostatic pressure tensor and shear deformation tensor, invariants
12. 16. Mai (PDF) strain tensor, rotation tensor, principal coefficients and principal directions;
uniform compression and shear deformation; elasticity tensor, Hooke's law
13. 23. Mai (PDF) electrical conductivity tensor, heat conductivity tensor;
contravariance of stress tensor
14. 30. Mai (PDF) review / discussion / exercises

Provisorischer Inhalt - Tentative plan

Course homepage:

Dozierende: Ana Cannas

Stand: 23. Mai 2012