# Advanced Linear Algebra

- Institution: IIT Roorkee
- Department: Mathematics
- Teacher: Prof. Premananda Bera
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111107164)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111107164)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Lecture 01| System of Linear Equations| Prof. Premananda Bera| IIT Roorkee| NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/09440e99ff52) (Video)
2. [Lecture 02| Elementary Row Operations| Prof. Premananda Bera| IIT Roorkee| NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/1e99dadc1d84) (Video)
3. [Lecture 03|Row-Reduced Echelon Form and its Applications|Prof. Premananda Bera|IIT Roorkee|NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/7e8562912433) (Video)
4. [Lecture 04| Vector Spaces-I| Prof. Premananda Bera| IIT Roorkee| NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/5969272f2ef8) (Video)
5. [Lecture 05| Vector Spaces-II| Prof. Premananda Bera| IIT Roorkee| NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/9ea734026329) (Video)
6. [Lecture 06| Basis and Dimensions-I| Prof. Premananda Bera| IIT Roorkee| NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/fa4ac798d566) (Video)
7. [Lecture 07|Basis and Dimensions-II| Prof. Premananda Bera| IIT Roorkee| NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/701d9e9620e5) (Video)
8. [Lecture 08| Change of Ordered Basis in F. D. V. S.| Prof. Premananda Bera| IIT Roorkee| NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/16d9c712dd48) (Video)
9. [Lecture 09| Row Space of a Matrix| Prof. Premananda Bera| IIT Roorkee| NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/a9b4c3d84973) (Video)
10. [Lecture 10| Computations concerning Subspaces| Prof. Premananda Bera| IIT Roorkee| NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/d8f09521cda6) (Video)
11. [Lecture 11| Linear Transformations| Prof. Premananda Bera| IIT Roorkee| NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/e9948a8356d8) (Video)
12. [Lecture 12| Concept of Rank| Prof. Premananda Bera| IIT Roorkee| NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/fcab03fc7d1e) (Video)
13. [Lecture 13| Algebra of Linear Transformations-I| Prof. Premananda Bera| IIT Roorkee| NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/c742d153b31e) (Video)
14. [Lecture 14| Algebra of Linear Transformations-II| Prof. Premananda Bera| IIT Roorkee| NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/23ef29e0e3d5) (Video)
15. [Lecture 15| Algebra of Linear Transformations-III| Prof. Premananda Bera| IIT Roorkee| NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/0ad5ffdbd689) (Video)
16. [Lecture 16|Matrix Representation of Linear Transformations-I|Prof. Premananda Bera|IIT Roorkee|NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/6b98c2fdcbe5) (Video)
17. [Lecture 17|Matrix Representation of Linear Transformation-II|Prof. Premananda Bera|IIT Roorkee|NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/1aa0fc4a29e7) (Video)
18. [Lecture 18| Linear Functional-I| Prof. Premananda Bera| IIT Roorkee| NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/b8802c1266ce) (Video)
19. [Lecture 19| Linear Functional-II| Prof. Premananda Bera| IIT Roorkee| NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/e51065f410a9) (Video)
20. [Lecture 20| Linear Functional-III| Prof. Premananda Bera| IIT Roorkee| NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/c7159f708bc6) (Video)
21. [Lecture 21 | Linear Functional & Transpose of L.T. - I | Prof. Premananda Bera | IIT Roorkee | NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/595df36e6024) (Video)
22. [Lecture 22 | Linear Functional & Transpose of L. T. - II |Prof. Premananda Bera | IIT Roorkee| NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/eb15965f18bc) (Video)
23. [Lecture 23|Eigenvalue & Eigenvector of Linear Operator - I |Prof. Premananda Bera| IIT Roorkee|NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/af11a44af1c0) (Video)
24. [Lecture 24|Eigenvalue & Eigenvector of Linear Operator - II |Prof. Premananda Bera|IIT Roorkee|NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/73d8ce81412f) (Video)
25. [Lecture 25| Eigenvalue & Eigenvector of Digonalizable L. O.|Prof. Premananda Bera| IIT Roorkee|NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/30a142f239ea) (Video)
26. [Lecture 26 | Annihilating Polynomial of Linear Operator | Prof. Premananda Bera | IIT Roorkee|NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/277acbc5d5c9) (Video)
27. [Lecture 27|Cayley-Hamilton Theorem and Its Applications - I |Prof. Premananda Bera|IIT Roorkee|NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/4de8edd302d5) (Video)
28. [Lecture 28|Cayley-Hamilton Theorem and its Applications - II|Prof. Premananda Bera|IIT Roorkee|NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/33d51e9fddef) (Video)
29. [Lecture 29| Invariant Subspaces - I | Prof. Premananda Bera| IIT Roorkee|NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/e2415c869bc2) (Video)
30. [Lecture 30| Invariant Subspaces - II | Prof. Premananda Bera | IIT Roorkee|NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/083c2a66bc49) (Video)
31. [Lecture 31 | Application of Invariant Subspaces - I | Prof. Premananda Bera | IIT Roorkee | NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/1c35fc7dd3d1) (Video)
32. [Lecture 32 | Application of Invariant Subspaces - II | Prof. Premananda Bera | IIT Roorkee | NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/6642ac0dfaf2) (Video)
33. [Lecture 33 | Direct Sum Decompositions - I | Prof. Premananda Bera | IIT Roorkee | NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/88fa364f6341) (Video)
34. [Lecture 34 | Direct Sum Decompositions - II | Prof. Premananda Bera | IIT Roorkee | NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/239969fc4d3f) (Video)
35. [Lecture 35 | Invariant Direct Sums - I | Prof. Premananda Bera | IIT Roorkee | NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/e31d5c038428) (Video)
36. [Lecture 36| Invariant Direct Sums - II | Prof. Premananda Bera| IIT Roorkee| NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/1e7f8264313a) (Video)
37. [Lecture 37 | Decomposition of space and Operator - I | Prof. Premananda Bera | IIT Roorkee | NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/ea0609309562) (Video)
38. [Lecture 38 | Decomposition of Space and Operator - II | Prof. Premananda Bera| IIT Roorkee|NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/d5934ae60a97) (Video)
39. [Lecture 39|Applications of Primary Decomposition Theorem - I|Prof. Premananda Bera|IIT Roorkee|NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/602ffd9dab28) (Video)
40. [Lecture 40|Applications of Primary Decomposition Theorem- II|Prof. Premananda Bera|IIT Roorkee|NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/0fcc39cd97d4) (Video)
41. [Lecture 41|Applications of Primary Decomposition Theorem-III |Prof Premananda Bera|IIT Roorkee|NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/5749c8381aa2) (Video)
42. [Lecture 42| Inner Products - I |Prof Premananda Bera | IIT Roorkee | NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/8ead8530e1bc) (Video)
43. [Lecture 43 | Inner Products - II | Prof. Premananda Bera | IIT Roorkee | NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/66161d80da39) (Video)
44. [Lecture 44| Inner Product Spaces - I |Prof Premananda Bera | IIT Roorkee | NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/5995facd39c6) (Video)
45. [Lecture 45 | Inner Product Spaces - II |Prof Premananda Bera | IIT Roorkee | NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/e154da9d3758) (Video)
46. [Lecture 46 | Best Approximation in I.P.S. |Prof Premananda Bera | IIT Roorkee | NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/7ee7a96b74e8) (Video)
47. [Lecture 47 | Orthogonal Projection in I.P.S. |Prof. Premananda Bera | IIT Roorkee | NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/0e7bb85c9cb1) (Video)
48. [Lecture 48 | Linear Functionals and Adjoints - I |Prof Premananda Bera | IIT Roorkee | NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/995d67a4b66d) (Video)
49. [Lecture 49 | Linear Functionals and Adjoints - II |Prof Premananda Bera | IIT Roorkee | NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/547f49f97a07) (Video)
50. [Lecture 50 | Linear Functionals and Adjoints - III |Prof Premananda Bera | IIT Roorkee | NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/cd04701db908) (Video)
51. [Lecture 51 | Linear Functionals and Adjoints - IV |Prof. Premananda Bera | IIT Roorkee | NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/4f31079cc067) (Video)
52. [Lecture 52 | Isomorphism in Inner Product Spaces |Prof. Premananda Bera | IIT Roorkee | NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/f0b1225f5392) (Video)
53. [Lecture 53 | Unitary Operators - I |Prof. Premananda Bera | IIT Roorkee | NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/fd75d791f921) (Video)
54. [Lecture 54 | Unitary Operators - II | Prof Premananda Bera | IIT Roorkee | NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/3da33de52991) (Video)
55. [Lecture 55|Application of Unitary O. & Initiation of Normal Operator |Prof P. Bera|IIT Roorkee|NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/2ad58adad631) (Video)
56. [Lecture 56 | Normal Operator - I | Prof Premananda Bera | IIT Roorkee | NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/8b0e66271a2d) (Video)
57. [Lecture 57 | Normal Operator - II | Prof. Premananda Bera | IIT Roorkee | NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/95cf2533683d) (Video)
58. [Lecture 58 | Normal Operator and It’s Spectral Resolution | Prof Premananda Bera | IIT Roorkee|NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/8ee8be4c0aab) (Video)
59. [Lecture 59 | Singular Value Decomposition of a Matrix | Prof Premananda Bera | IIT Roorkee | NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/ce0f4ed029b7) (Video)
60. [Lecture 60 | Forms on Inner product Spaces | Prof Premananda Bera | IIT Roorkee | NPTEL](https://invisiblenetwork.ai/learn/nptel/111107164/b3ab42aaf0e3) (Video)