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Course11110716460 lectures

Advanced Linear Algebra

Prof. Premananda Bera · IIT Roorkee

Start with lecture 1 At NPTEL

Lectures

week-01

  1. Lecture 01| System of Linear Equations| Prof. Premananda Bera| IIT Roorkee| NPTEL Video
  2. Lecture 02| Elementary Row Operations| Prof. Premananda Bera| IIT Roorkee| NPTEL Video
  3. Lecture 03|Row-Reduced Echelon Form and its Applications|Prof. Premananda Bera|IIT Roorkee|NPTEL Video
  4. Lecture 04| Vector Spaces-I| Prof. Premananda Bera| IIT Roorkee| NPTEL Video
  5. Lecture 05| Vector Spaces-II| Prof. Premananda Bera| IIT Roorkee| NPTEL Video

week-02

  1. Lecture 06| Basis and Dimensions-I| Prof. Premananda Bera| IIT Roorkee| NPTEL Video
  2. Lecture 07|Basis and Dimensions-II| Prof. Premananda Bera| IIT Roorkee| NPTEL Video
  3. Lecture 08| Change of Ordered Basis in F. D. V. S.| Prof. Premananda Bera| IIT Roorkee| NPTEL Video
  4. Lecture 09| Row Space of a Matrix| Prof. Premananda Bera| IIT Roorkee| NPTEL Video
  5. Lecture 10| Computations concerning Subspaces| Prof. Premananda Bera| IIT Roorkee| NPTEL Video

week-03

  1. Lecture 11| Linear Transformations| Prof. Premananda Bera| IIT Roorkee| NPTEL Video
  2. Lecture 12| Concept of Rank| Prof. Premananda Bera| IIT Roorkee| NPTEL Video
  3. Lecture 13| Algebra of Linear Transformations-I| Prof. Premananda Bera| IIT Roorkee| NPTEL Video
  4. Lecture 14| Algebra of Linear Transformations-II| Prof. Premananda Bera| IIT Roorkee| NPTEL Video
  5. Lecture 15| Algebra of Linear Transformations-III| Prof. Premananda Bera| IIT Roorkee| NPTEL Video

week-04

  1. Lecture 16|Matrix Representation of Linear Transformations-I|Prof. Premananda Bera|IIT Roorkee|NPTEL Video
  2. Lecture 17|Matrix Representation of Linear Transformation-II|Prof. Premananda Bera|IIT Roorkee|NPTEL Video
  3. Lecture 18| Linear Functional-I| Prof. Premananda Bera| IIT Roorkee| NPTEL Video
  4. Lecture 19| Linear Functional-II| Prof. Premananda Bera| IIT Roorkee| NPTEL Video
  5. Lecture 20| Linear Functional-III| Prof. Premananda Bera| IIT Roorkee| NPTEL Video

week-05

  1. Lecture 21 | Linear Functional & Transpose of L.T. - I | Prof. Premananda Bera | IIT Roorkee | NPTEL Video
  2. Lecture 22 | Linear Functional & Transpose of L. T. - II |Prof. Premananda Bera | IIT Roorkee| NPTEL Video
  3. Lecture 23|Eigenvalue & Eigenvector of Linear Operator - I |Prof. Premananda Bera| IIT Roorkee|NPTEL Video
  4. Lecture 24|Eigenvalue & Eigenvector of Linear Operator - II |Prof. Premananda Bera|IIT Roorkee|NPTEL Video
  5. Lecture 25| Eigenvalue & Eigenvector of Digonalizable L. O.|Prof. Premananda Bera| IIT Roorkee|NPTEL Video

week-06

  1. Lecture 26 | Annihilating Polynomial of Linear Operator | Prof. Premananda Bera | IIT Roorkee|NPTEL Video
  2. Lecture 27|Cayley-Hamilton Theorem and Its Applications - I |Prof. Premananda Bera|IIT Roorkee|NPTEL Video
  3. Lecture 28|Cayley-Hamilton Theorem and its Applications - II|Prof. Premananda Bera|IIT Roorkee|NPTEL Video
  4. Lecture 29| Invariant Subspaces - I | Prof. Premananda Bera| IIT Roorkee|NPTEL Video
  5. Lecture 30| Invariant Subspaces - II | Prof. Premananda Bera | IIT Roorkee|NPTEL Video

week-07

  1. Lecture 31 | Application of Invariant Subspaces - I | Prof. Premananda Bera | IIT Roorkee | NPTEL Video
  2. Lecture 32 | Application of Invariant Subspaces - II | Prof. Premananda Bera | IIT Roorkee | NPTEL Video
  3. Lecture 33 | Direct Sum Decompositions - I | Prof. Premananda Bera | IIT Roorkee | NPTEL Video
  4. Lecture 34 | Direct Sum Decompositions - II | Prof. Premananda Bera | IIT Roorkee | NPTEL Video
  5. Lecture 35 | Invariant Direct Sums - I | Prof. Premananda Bera | IIT Roorkee | NPTEL Video

week-08

  1. Lecture 36| Invariant Direct Sums - II | Prof. Premananda Bera| IIT Roorkee| NPTEL Video
  2. Lecture 37 | Decomposition of space and Operator - I | Prof. Premananda Bera | IIT Roorkee | NPTEL Video
  3. Lecture 38 | Decomposition of Space and Operator - II | Prof. Premananda Bera| IIT Roorkee|NPTEL Video
  4. Lecture 39|Applications of Primary Decomposition Theorem - I|Prof. Premananda Bera|IIT Roorkee|NPTEL Video
  5. Lecture 40|Applications of Primary Decomposition Theorem- II|Prof. Premananda Bera|IIT Roorkee|NPTEL Video

week-09

  1. Lecture 41|Applications of Primary Decomposition Theorem-III |Prof Premananda Bera|IIT Roorkee|NPTEL Video
  2. Lecture 42| Inner Products - I |Prof Premananda Bera | IIT Roorkee | NPTEL Video
  3. Lecture 43 | Inner Products - II | Prof. Premananda Bera | IIT Roorkee | NPTEL Video
  4. Lecture 44| Inner Product Spaces - I |Prof Premananda Bera | IIT Roorkee | NPTEL Video
  5. Lecture 45 | Inner Product Spaces - II |Prof Premananda Bera | IIT Roorkee | NPTEL Video

week-10

  1. Lecture 46 | Best Approximation in I.P.S. |Prof Premananda Bera | IIT Roorkee | NPTEL Video
  2. Lecture 47 | Orthogonal Projection in I.P.S. |Prof. Premananda Bera | IIT Roorkee | NPTEL Video
  3. Lecture 48 | Linear Functionals and Adjoints - I |Prof Premananda Bera | IIT Roorkee | NPTEL Video
  4. Lecture 49 | Linear Functionals and Adjoints - II |Prof Premananda Bera | IIT Roorkee | NPTEL Video
  5. Lecture 50 | Linear Functionals and Adjoints - III |Prof Premananda Bera | IIT Roorkee | NPTEL Video

week-11

  1. Lecture 51 | Linear Functionals and Adjoints - IV |Prof. Premananda Bera | IIT Roorkee | NPTEL Video
  2. Lecture 52 | Isomorphism in Inner Product Spaces |Prof. Premananda Bera | IIT Roorkee | NPTEL Video
  3. Lecture 53 | Unitary Operators - I |Prof. Premananda Bera | IIT Roorkee | NPTEL Video
  4. Lecture 54 | Unitary Operators - II | Prof Premananda Bera | IIT Roorkee | NPTEL Video
  5. Lecture 55|Application of Unitary O. & Initiation of Normal Operator |Prof P. Bera|IIT Roorkee|NPTEL Video

week-12

  1. Lecture 56 | Normal Operator - I | Prof Premananda Bera | IIT Roorkee | NPTEL Video
  2. Lecture 57 | Normal Operator - II | Prof. Premananda Bera | IIT Roorkee | NPTEL Video
  3. Lecture 58 | Normal Operator and It’s Spectral Resolution | Prof Premananda Bera | IIT Roorkee|NPTEL Video
  4. Lecture 59 | Singular Value Decomposition of a Matrix | Prof Premananda Bera | IIT Roorkee | NPTEL Video
  5. Lecture 60 | Forms on Inner product Spaces | Prof Premananda Bera | IIT Roorkee | NPTEL Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Roorkee
Department
Mathematics
Teacher
Prof. Premananda Bera
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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