Videos and examples from lectures LA I
Video lectures
- Introduction
Course overview (2:12, 312M)
smaller version (6M)
- Applications
Applications in practice (31:57, 1.15G)
- slides only,
smaller version (47M)
- 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)
- Matrices
Matrix operations, regular matrix, inverse matrix (41:02, 817M)
- slides only,
smaller version (77M)
- 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)
- Fields
Fields, properties, characteristic, Fermat's little theorem (30:50, 66M)
- slides only,
smaller version (36M)
- 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)
- 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)
- 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.)
Examples