# Videos and examples from lectures LA I

## Video lectures

1. Introduction
Course overview (2:12, 312M) smaller version (6M)
2. Applications
Applications in practice (31:57, 1.15G) - slides only, smaller version (47M)
3. Systems of linear equations
Systems of linear equations, elementary transformations (29:52, 441M) - slides only, smaller version (43M)
Corrected (RREF -> REF): Gaussian elimination (18:40, 44M) - slides only, smaller version (22M)
Describing all solutions (31:02, 518M) - slides only, smaller version (47M)
4. Matrices
Matrix operations, regular matrix, inverse matrix (41:02, 817M) - slides only, smaller version (77M)
5. Groups
Groups, abelian, additive, multiplicative (16:14, 213M) - slides only, smaller version (22M)
Retaken: Permutations, inversion, transposition, sign (20:08, 326M) - slides only, smaller version (36M)
Optional topic: Subgroups, cosets, quotient groups (31:43, 68M) - slides only, smaller version (37M)
6. Fields
Fields, properties, characteristic, Fermat's little theorem (30:50, 66M) - slides only, smaller version (36M)
7. Vector spaces
Vector spaces, properties, subspaces, linear hull, matrix spaces (43:42, 540M) - slides only, smaller version (73M)
Linear independence, bases, exchange theorem, dimension (32:57, 733M) - slides only, smaller version (65M)
Row and column space of a matrix and their dimension (12:39, 347M) - slides only, smaller version (27M)
8. Linear maps
Linear maps, affine subspaces (20:18, 545M) - slides only, smaller version (45M)
Matrices of linear maps, basis change, isomorphism (29:52, 534M) - slides only, smaller version (50M)
9. Applications
Number of even subgraphs (6:10, 13M) - slides only, smaller version (7M)
Constrained set systems (4:51, 9M) - slides only, smaller version (5M)
Partition of a rectangle (7:00, 17M) - slides only, smaller version (8M)
(The small versions may have sound problems on some devices.)