# Linear Algebra

- Institution: IIT Madras
- Department: Mathematics
- Teacher: Dr. K.C. Sivakumar
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111106051)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111106051)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [1. Introduction to the Course Contents.](https://invisiblenetwork.ai/learn/nptel/111106051/36b7d8d219c7) (Video)
2. [2. Linear Equations](https://invisiblenetwork.ai/learn/nptel/111106051/3f817d759edf) (Video)
3. [3a. Equivalent Systems of Linear Equations I: Inverses of Elementary Row-operations, Row-equivalent matrices](https://invisiblenetwork.ai/learn/nptel/111106051/462d68bff022) (Video)
4. [3b. Equivalent Systems of Linear Equations II: Homogeneous Equations, Examples](https://invisiblenetwork.ai/learn/nptel/111106051/6c051866802d) (Video)
5. [4. Row-reduced Echelon Matrices](https://invisiblenetwork.ai/learn/nptel/111106051/e7eacf18867b) (Video)
6. [5. Row-reduced Echelon Matrices and Non-homogeneous Equations](https://invisiblenetwork.ai/learn/nptel/111106051/e12eb3d21701) (Video)
7. [6. Elementary Matrices, Homogeneous Equations and Non-homogeneous Equations](https://invisiblenetwork.ai/learn/nptel/111106051/7181a6717852) (Video)
8. [7. Invertible matrices, Homogeneous Equations Non-homogeneous Equations](https://invisiblenetwork.ai/learn/nptel/111106051/f6c9bd83bcb1) (Video)
9. [8. Vector spaces](https://invisiblenetwork.ai/learn/nptel/111106051/e4b2b20abd9d) (Video)
10. [9. Elementary Properties in Vector Spaces. Subspaces](https://invisiblenetwork.ai/learn/nptel/111106051/4c73057d57a4) (Video)
11. [10. Subspaces (continued), Spanning Sets, Linear Independence, Dependence](https://invisiblenetwork.ai/learn/nptel/111106051/75f578e23ae0) (Video)
12. [11. Basis for a vector space](https://invisiblenetwork.ai/learn/nptel/111106051/8113fc354f1b) (Video)
13. [12. Dimension of a vector space](https://invisiblenetwork.ai/learn/nptel/111106051/298080f5095f) (Video)
14. [13. Dimensions of Sums of Subspaces](https://invisiblenetwork.ai/learn/nptel/111106051/deb8fcf4d7ff) (Video)
15. [14. Linear Transformations](https://invisiblenetwork.ai/learn/nptel/111106051/fca445928990) (Video)
16. [15. The Null Space and the Range Space of a Linear Transformation](https://invisiblenetwork.ai/learn/nptel/111106051/db1f69f9a6ae) (Video)
17. [16. The Rank-Nullity-Dimension Theorem. Isomorphisms Between Vector Spaces](https://invisiblenetwork.ai/learn/nptel/111106051/24761c641b4f) (Video)
18. [17. Isomorphic Vector Spaces, Equality of the Row-rank and the Column-rank I](https://invisiblenetwork.ai/learn/nptel/111106051/97f087c20f98) (Video)
19. [18. Equality of the Row-rank and the Column-rank II](https://invisiblenetwork.ai/learn/nptel/111106051/d7a0208d599d) (Video)
20. [19. The Matrix of a Linear Transformation](https://invisiblenetwork.ai/learn/nptel/111106051/0bfdc91e69ec) (Video)
21. [20. Matrix for the Composition and the Inverse. Similarity Transformation](https://invisiblenetwork.ai/learn/nptel/111106051/a551280ccb72) (Video)
22. [21. Linear Functionals. The Dual Space. Dual Basis I](https://invisiblenetwork.ai/learn/nptel/111106051/6dfb1b4da837) (Video)
23. [22. Dual Basis II. Subspace Annihilators I](https://invisiblenetwork.ai/learn/nptel/111106051/d45858a2e871) (Video)
24. [23. Subspace Annihilators II](https://invisiblenetwork.ai/learn/nptel/111106051/65ce598d1e92) (Video)
25. [24. The Double Dual. The Double Annihilator](https://invisiblenetwork.ai/learn/nptel/111106051/04e8161c4b1f) (Video)
26. [25. The Transpose of a Linear Transformation. Matrices of a Linear Transformation and its Transpose](https://invisiblenetwork.ai/learn/nptel/111106051/fc56d03c902f) (Video)
27. [26. Eigenvalues and Eigenvectors of Linear Operators](https://invisiblenetwork.ai/learn/nptel/111106051/8b3c775e53c6) (Video)
28. [27. Diagonalization of Linear Operators. A Characterization](https://invisiblenetwork.ai/learn/nptel/111106051/a6db3c0fd002) (Video)
29. [28. The Minimal Polynomial](https://invisiblenetwork.ai/learn/nptel/111106051/63a3acc350e9) (Video)
30. [29. The Cayley-Hamilton Theorem](https://invisiblenetwork.ai/learn/nptel/111106051/22ee77823e25) (Video)
31. [30. Invariant Subspaces](https://invisiblenetwork.ai/learn/nptel/111106051/118dca0c868b) (Video)
32. [31. Triangulability, Diagonalization in Terms of the Minimal Polynomial](https://invisiblenetwork.ai/learn/nptel/111106051/c036bffbf654) (Video)
33. [32. Independent Subspaces and Projection Operators](https://invisiblenetwork.ai/learn/nptel/111106051/6a237c45f95d) (Video)
34. [33. Direct Sum Decompositions and Projection Operators I](https://invisiblenetwork.ai/learn/nptel/111106051/abc05b1a23d0) (Video)
35. [34. Direct Sum Decomposition and Projection Operators II](https://invisiblenetwork.ai/learn/nptel/111106051/bcaaaaba6973) (Video)
36. [35. The Primary Decomposition Theorem and Jordan Decomposition](https://invisiblenetwork.ai/learn/nptel/111106051/d41da1a8ce5d) (Video)
37. [36. Cyclic Subspaces and Annihilators](https://invisiblenetwork.ai/learn/nptel/111106051/1af4e0e3381b) (Video)
38. [37. The Cyclic Decomposition Theorem I](https://invisiblenetwork.ai/learn/nptel/111106051/93fe049f6a8a) (Video)
39. [38. The Cyclic Decomposition Theorem II. The Rational Form](https://invisiblenetwork.ai/learn/nptel/111106051/5d8c2212fa02) (Video)
40. [39. Inner Product Spaces](https://invisiblenetwork.ai/learn/nptel/111106051/777ea2f5041e) (Video)
41. [40. Norms on Vector spaces. The Gram-Schmidt Procedure I](https://invisiblenetwork.ai/learn/nptel/111106051/7f8019792a6a) (Video)
42. [41. The Gram-Schmidt Procedure II. The QR Decomposition.](https://invisiblenetwork.ai/learn/nptel/111106051/b7f9bb66c7a9) (Video)
43. [42. Bessel's Inequality, Parseval's Indentity, Best Approximation](https://invisiblenetwork.ai/learn/nptel/111106051/de6b8299d36d) (Video)
44. [43. Best Approximation: Least Squares Solutions](https://invisiblenetwork.ai/learn/nptel/111106051/79b14f3ab6dc) (Video)
45. [44. Orthogonal Complementary Subspaces, Orthogonal Projections](https://invisiblenetwork.ai/learn/nptel/111106051/e02aabf05464) (Video)
46. [45. Projection Theorem. Linear Functionals](https://invisiblenetwork.ai/learn/nptel/111106051/5a8bd6f70be7) (Video)
47. [46. The Adjoint Operator](https://invisiblenetwork.ai/learn/nptel/111106051/ea33c6820353) (Video)
48. [47. Properties of the Adjoint Operation. Inner Product Space Isomorphism](https://invisiblenetwork.ai/learn/nptel/111106051/0dbe844298c0) (Video)
49. [48. Unitary Operators](https://invisiblenetwork.ai/learn/nptel/111106051/a2145339f4ee) (Video)
50. [49. Unitary operators II. Self-Adjoint Operators I.](https://invisiblenetwork.ai/learn/nptel/111106051/664e2355947b) (Video)
51. [50. Self-Adjoint Operators II - Spectral Theorem](https://invisiblenetwork.ai/learn/nptel/111106051/fc25c9aaa745) (Video)
52. [51. Normal Operators - Spectral Theorem](https://invisiblenetwork.ai/learn/nptel/111106051/bfc23a207d9a) (Video)