|
Lecture
1
(August 04, 2003)
|
Review of set theory |
|
Lecture
2 (August
06, 2003)
|
Algebraic Preliminaries |
|
Lecture
3 (August
08, 2003)
|
Vector Spaces |
|
Lecture
4 (August
11, 2003)
|
Subspaces |
|
Lecture
5 (August
13, 2003) |
Generating
systems |
|
Lecture
6 (August
18, 2003)
|
System of linear equations
-- Gauss elimination |
|
Lecture 7
(August
20, 2003)
|
Linear independence |
|
Lecture 8
(August
22, 2003)
|
Maximal generating systems,
Minimal linear independent subsets -- Set
theory -- Zorn's lemma |
|
Lecture 9
(August
25, 2003)
|
Bases, Dimension of vector
spaces -- Set theory
-- cardinal numbers and their arithmetic |
|
Lecture 10
(August
27, 2003)
|
Dimension of vector
spaces |
|
Lecture 11
(August
29, 2003) |
Affine Spaces
-- Concept of
Affine spaces, Affine subspaces |
|
Lecture 12
(September
01, 2003) |
Affine Subpaces -- Continued |
|
Lecture 13
(September
03, 2003) |
Linear maps -- Group
Homomorphisms, Linear Maps |
|
Lecture 14
(September
05, 2003) |
Space of Linear Maps |
|
Lecture 15
(September
08, 2003) |
Linear Maps
and bases |
|
Lecture 16
(September
10, 2003) |
Rank Theorem |
|
Lecture 17
(September
12, 2003) |
Direct Sums and
Projections, Dual Spaces |
|
*Lecture 18
(September
13, 2003) |
Affine Maps |
|
Lecture 19
(September
15, 2003) |
Dual Spaces |
|
Lecture 20
(September
17, 2003) |
Quotient Spaces
- - Isomorphism theorems, Exact Sequences |
|
Lecture 21
(September
19, 2003) |
Group actions |
|
*Lecture 22
(September
20, 2003) |
Affine Maps --
Continued |
|
Lecture 23
(September
22, 2003) |
Group actions
--
Continued |
|
Lecture 24
(September
24, 2003) |
Matrices --
The Matrix of a Linear Map, Properties of matrices. Matrix algebra. |
|
Lecture 25
(September
26, 2003) |
Matrices --
Continued -- Transition matrices, Change of basis --Similar
matrices. |
|
Lecture 26
(October
01, 2003) |
Matrices --
Continued -- Matrix of a dual map |
|
Lecture 27
(October
05, 2003) |
Matrices --
Continued -- Rank of matrices, Row and column ranks, Elementary
operations |
|
Lecture 28
(October
06, 2003) |
Matrices --
Continued -- Triangular matrices, nilpotent operators |
|
Lecture 29
(October
09, 2003) |
Matrices --
Continued -- Elementary Matrices. |
|
Lecture 30
(October
10, 2003) |
Matrices --
Continued -- Elementary divisor theorem. |
|
Lecture 31
(October
13, 2003) |
Applications of
Elementary divisors theorem
--- Structure of
finitely generated abelain groups, Linear system of Diophantine equations |
|
Lecture 32
(October
14, 2003) |
Permutations. |
|
Lecture 33
(October
15, 2003) |
Permutations
--Continued |
|
Lecture 34
(October
17, 2003) |
Multilinear and
alternating maps. |
|
Lecture 35
(October
20, 2003) |
Determinants -
- Determinant functions |
|
Lecture 36
(October
22, 2003) |
Rules for
computations -- Minor criterion for
rank, Elementary operations |
|
Lecture 37
(October
24, 2003) |
Expansions of
determinants, Cramer's Rule |
|
Lecture 38
(October
27, 2003) |
Orientations |
|
Lecture 39
(October
29, 2003) |
Volume and
Determinants |
|
Lecture 40
(October
31, 2003) |
Eigen values,
Spectral values, Minimal polynomials of linear operators |
|
Lecture 41
(November
03, 2003) |
Characteristic
polynomial, Cayley-Hamilton theorem |
|
Lecture 42
(November
05, 2003) |
Prime divisors of
Characteristic and Minimal polynomials. |
|
Lecture 43
(November
07, 2003) |
Examples --
Eigenvalues, Spectral
values,
Characteristic and Minimal polynomials. |
|
Lecture 44
(November
10, 2003) |
Diagonalisable and
triangulable operators |
|
Lecture 45
(November
12, 2003) |
Primary
decomposition theorem |
|
Lecture 46
(November
14, 2003) |
Additive and
multiplicative canonical decompositions |
|
Lecture 47
(November
17, 2003) |
Jordon canonical
form over algebraically closed fields |
|
Lecture 48
(November
19, 2003) |
Jordon canonical
form over arbitrary fields ---
In particular over the
field of real numbers |
|
Lecture 49
(November
21, 2003) |
|
|
Lecture 50
(November
24, 2003) |
|
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