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Module 1: Basics of Linear Algebra
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Lecture 1A - Why Study Linear Algebra
22:00
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Lecture 1B - Linear Algebra for GATE & Interviews
14:00
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Annotated Notes - Lecture 1A-1B
(32 pages)
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Lecture 1C - Linearly Independent and Linearly Dependent
75:00
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Annotated Notes - Lecture 1C
(92 pages)
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Lecture 2A - Filling the Space Part 1
44:00
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Lecture 2B - Filling the Space Part 2
28:00
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Lecture 2C - Summary so far
12:00
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Lecture 2D - Multiplying a Matrix & a Vector
26:00
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Annotated Notes - Lecture 2
(103 pages)
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Homework 1 - Linear Dependence & Independence
(12 pages)
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Lecture 3A - Homework 1 Discussion
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Annotated Notes - Lecture 3A - Homework 1 Discussion
(20 pages)
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Lecture 3B - Why Solve System Of Linear Equations
22:00
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Lecture 3C - Writing as Ax=b, Geometric Interpretation and Possible Solutions
24:00
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Lecture 3D - Understanding Ax=b intuitively
44:00
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Lecture 3B-D Annotated Notes
(74 pages)
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4A. Multiplying 2 Matrices | My Walmart Interview Question
18:00
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4B. GATE 2016 Question
16:00
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4C. GATE 2014 Question
14:00
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4D. Two conceptual questions
28:00
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4E. Linear Combination of Independent vectors is unique
28:00
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4F. GATE 2017 Question
4:00
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Lecture 4 Annotated Notes
(76 pages)
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5A. Echelon Form and Pivot Columns
37:00
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5B. Gaussian Elimination
26:00
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5C. Rank | GATE 1994 Question | Rank Nullity Theorem
11:00
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5D. Finally Solving Ax=b | Five Different Questions
33:00
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5E. More than one free variable in 𝐴𝑥=0 solution
32:00
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Lecture 5 Annotated Notes
(125 pages)
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6A. GATE 2021 Question | Free variables in Non homogeneous
19:00
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6B. Solutions based on Rank(A) and Rank(A|b)
18:00
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6C. Few Questions related to rank(A) and Number of solutions
8:00
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6D. Linearly Independent Columns with Gaussian Elimination
24:00
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6E. Row Reduced Echelon Form
28:00
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Lecture 6 Annotated Notes
(74 pages)
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Lecture 7A. Determinant
100:00
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Lecture 7B. Inverse of a Matrix
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Lecture 7C. Crammer's rule
26:00
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Annotated Notes Lecture 7 A-C Determinant Inverse and Cramer's Rule
(149 pages)
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Lecture 8A. Introduction to Eigenvalues and Eigenvectors
23:00
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Lecture 8B. Characteristic Equation
15:00
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Lecture 8C. Solving for Eigenvalues and Eigenvectors
22:00
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Annotated Notes Lecture 8A-C EigenValues and EigenVectors
(45 pages)
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Lecture 9A. Linearly Independent Eigen vectors with repeating eigenvalues
21:00
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Lecture 9B. Three Different Examples With Repeating Lambda
30:00
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Lecture 9C. Symmetric Matrices has n LI Eigen Vectors
12:00
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Lecture 9D. Two Magical Properties
12:00
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Annotated Notes Lecture 9A-D Eigen Vectors
(95 pages)
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Lecture 10A. Rank and Eigen Values
22:00
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Lecture 10B. Examples on Rank and Eigen Values
15:00
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Lecture 10C. CAYLEY-HAMILTON THEOREM
16:00
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Lecture 10D. Eigen Values of AB and BA
32:00
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Lecture 10E. Eigen Values of Powers of A
17:00
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Annotated Notes Lecture 10A-E Rank and EigenValues
(99 pages)
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Lecture 10F. (Three Tough/Interesting GATE PYQs)
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Annotated Notes Lecture 10F GATE PYQs Linear Algebra
(14 pages)
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Lecture 11A. LU Decomposition
25:00
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Lecture 11B. Type Of Matrices
84:00
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Annotated Notes Lecture 11A -B
(80 pages)
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LIVE Practice Questions on Linear Dependent Vectors
62:00
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Annotated Notes Practice Questions on Linear Dependent Vectors
(59 pages)
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LIVE Practice Questions on Solutions of Ax = b
61:00
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Annotated Notes Practice Questions on Ax=b
(58 pages)
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Weekly Quiz and Solution
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Linear Algebra Weekly Quiz 4 Solutions
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Annotated Notes Weekly Quiz 4 Solution Linear Algebra
(45 pages)
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Module 2
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Information about the Module 2
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Lecture 1A: Introduction to Vector Space
31:00
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Lecture 1B: Questions on Vector Space | GATE DA 2024 Question | IIT JAM Question
20:00
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Annotated Notes Lecture 1A,B Vector Space
(50 pages)
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Lecture 2A. Subspace Of a Vector Space
37:00
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Lecture 2B. Questions on Subspace Of a Vector Space
21:00
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Lecture 2C. Basis and Span of a Vector Space
59:00
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Annotated Notes - Lec 2A, 2B, 2C Linear Algebra DA
(127 pages)
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Lecture 3A. Questions on Vector Spaces | IIT JAM 2014, 2016, GATE DA 2024
30:00
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Lecture 3B. Introduction to Column Space and Null Space
34:00
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Lecture 3C. More Questions on Column Space and Null Space
25:00
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Annotated Notes - Lec 3A, 3B, 3C Linear Algebra DA
(80 pages)
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Lecture 4A. Row Space of a MAtrix
21:00
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Lecture 4B. Left Null Space of a Matrix
16:00
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Lecture 4C. More Questions on Four Spaces of a Matrix
34:00
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Annotated Notes Lecture 4 Module 2 Row and Left Null Space
(75 pages)
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Lecture 5A. More Questions on Four Fundamental Subspaces
28:00
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Lecture 5B. IIT JAM 2016 Question and Other Questions
14:00
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Lecture 5C. Important Questions and Important Results to Remember
10:00
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Lecture 5D. The Big Picture of Four Fundamental Spaces
19:00
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Annotated Notes Lecture 5 Module 2 Four Fundamental Subspaces
(71 pages)
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Lecture 6A. Introduction to Change Of Basis
35:00
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Lecture 6B. More Questions on Change Of Basis
24:00
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Lecture 6C. Even More Questions on Change Of Basis
23:00
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Annotated NotesLecture 6 Change Of Basis
(76 pages)
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Lecture 7A. Introduction to Linear Transformation
38:00
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Lecture 7B. More Questions on Linear Transformation
9:00
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Lecture 7C. The Matrix of Linear Transformation
36:00
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Lecture 7D. Question on the Matrix of Linear Transformation
7:00
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Lecture 7E. More Questions on the Matrix of Linear Transformation
28:00
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Annotated Notes Lecture 7 Linear Transformation
(115 pages)
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Lecture 8A. Types of Different Functions
23:00
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Lecture 8B. Types of Different Linear Transformations
30:00
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Lecture 8C. Linear Transformation wrt a Basis
30:00
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Annotated Notes Lecture 8 Types of Different Functions and LTs
(109 pages)
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Lecture 9A. Question on Matrix of Linear Transformation
19:00
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Lecture 9B. 2nd Approach to get Matrix of Linear Transformation
17:00
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Lecture 9C. More Questions using 2nd Approach | MIT Question
30:00
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Lecture 9D. Single Question to clear All Concepts and Confusions
6:00
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Lecture 9E. Even More Questions On Linear Transformation
16:00
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Annotated Notes Lecture 9 Matrix of Linear Transformation
(66 pages)
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Lecture 10A. Beautiful Proof for Change of Basis and Linear Transformation Matrices
29:00
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Lecture 10B. More Questions on Linear Transformation using Second Method
31:00
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Lecture 10C. Even More Questions on Linear Transformation using Second Method
15:00
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Annotated Notes Lecture 10 Linear Transformation using Second Method
(58 pages)
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Linear Algebra Homework Questions
(19 pages)
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Lecture 11 A. Similar Matrices
35:00
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Lecture 11B. Diagonalisation of Matrices
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Lecture 11C. Geometric interpretation of Diagonalization of Matrices
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Annotated Notes Lecture 11 A,B,C Similar Matrices and Diagonalisation
(155 pages)
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Lecture 12. Projection and Gram–Schmidt Process
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Annotated Notes Lecture 12 Projection and Gram–Schmidt Process
(74 pages)
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Lecture 13. Singular Value Decomposition (SVD)
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Annotated Notes Lecture 13 SVD
(92 pages)
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14A. SVD as Summation of Rank-1 Matrices
28:00
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Lecture 14B. Geometry of SVD
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Annotated Notes Lecture 14 SVD as Summation of Rank 1 Matrices and Geoemtry of SVD
(72 pages)
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Lecture 15: Positive Definite Matrices
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Lecture 16: Introduction to Partition Matrix or Block Matrix
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Lecture 17: Operations using Partition Matrix or Block Matrix
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Lecture 18: Projection Matrix
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Annotated Notes Lecture 18 Projection Matrices
(50 pages)
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Lecture 19: Orthogonal Decomposition and Projection Matrices for Orthonormal Bases
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Annotated Notes Lecture 19 Orthogonal Decomposition and Projection Matrices for Orthonormal Bases
(66 pages)
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Lecture 20: More on Projection Matrices and 25 Questions on Projection Matrices
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Annotated Notes Lecture 20 Projection Matrices
(96 pages)
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Student Handwritten Notes
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Handwritten Notes Linear Algebra By Sajan GATE DA 2025 AIR 19
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