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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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Live Session 1 - Homework 1 Discussion
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Annotated Notes - Live Session 1
(20 pages)
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Lecture 3A - Why Solve System Of Linear Equations
22:00
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Lecture 3B - Writing as Ax=b, Geometric Interpretation and Possible Solutions
24:00
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Lecture 3C - Understanding Ax=b intuitively
44:00
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Lecture 3 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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Homework 2
(20 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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Live Session -2
94:00
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Live Session 2 Annotated Notes
(48 pages)
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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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Recording - Live Session -3
60:00
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Live Session -3
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Live Session 3 Annotated Notes
(18 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. [OPTIONAL] Linearly Independent Columns with Gaussian Elimination
24:00
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6e. [Optional] Row Reduced Echelon Form
28:00
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Lecture 6 Annotated Notes
(74 pages)
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Homework Questions Set 2
(20 pages)
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Lecture 7 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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Lecture 7 Annotated Notes
(149 pages)
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Lecture 8a. Introduction to Eigenvalues and Eigenvectors
23:00
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Lecture 8b. Characterstic Equation
15:00
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Lecture 8c. Solving for Eigenvalues and Eigenvectors
22:00
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Lecture 8 Annotated Notes
(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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Lecture 9 Annotated Notes
(95 pages)
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(New) Practice Questions based on Concepts covered upto lecture 4F
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Annotated Notes Practice Questions based on Concepts covered upto lecture 4F
(79 pages)
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(New) Practice Questions based on Concepts covered upto lecture 4F - Part2
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Annotated Notes Practice Questions based on Concepts covered upto lecture 4F Part2
(82 pages)
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10a. Rank and Eigen Values
22:00
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10b. Examples on Rank and Eigen Values
15:00
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10c. CAYLEY-HAMILTON THEOREM
16:00
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10d. Eigen Values of AB and BA
32:00
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10e. Eigen Values of Powers of A
17:00
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Lecture 10 Annotated Notes
(99 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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Lecture 11 Annotated Notes
(80 pages)
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Weekly Quiz 3 GATE 2025 Solution
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Annotated Notes Weekly Quiz 3 Linear Algebra
(64 pages)
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Module-2
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Lecture 1: Introduction to Vector Spaces, Subspaces, Basis, and Span
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Annotated Notes Lecture 1 Module 2 Definition of Vector Spaces and SubSpaces
(86 pages)
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Lecture 2: Basis, Span, Subspaces of Matrix A (Column and Null Space)
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Annotated Notes Lecture 2 Module 2 Basis Span and Dim of Space
(97 pages)
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Lecture 3: Subspaces of Matrix A (Column and Null Space)
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Annotated Notes Lecture 3 Module 2 Col and Null Space
(81 pages)
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Lecture 4: Subspaces of Matrix A (Row and Left Null Space)
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Annotated Notes Lecture 4 Module 2 Row and Left Null Space
(75 pages)
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LA for GATE DA Module-2 HomeWork-1
(32 pages)
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LA for GATE DA Module-2 HomeWork-2
(27 pages)
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Lecture 5: Four Fundamental Subspaces
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Annotated Notes Lecture 5 Module 2 Four Fundamental Subspaces
(71 pages)
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Lecture 6: Change of Basis
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Annotated Notes Lecture 6 Module 2 Change of Basis
(77 pages)
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Lecture 7: Linear Transformation
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Annotated Notes Lecture 7 Module 2 Linear Transformation
(81 pages)
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Lecture 8: More on Linear Transformation
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Annotated Notes Lecture 8 Module 2 More on Linear Transformation
(186 pages)
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Lecture 9: Linear Transformation w.r.t. arbitrary bases
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Annotated Notes Lecture 9 Module 2 Linear Transformation in different bases
(105 pages)
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Lecture 10: Questions on Change of Basis and Linear Transformation
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Annotated Notes Lecture 10 Module 2 Questions on Linear Transformation and change of bases
(58 pages)
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Weekly Quiz
(34 pages)
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Weekly Quiz-5 Solution Discussion
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Lecture 11a: Revision Class (From Lecture 1 to 5)
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Lecture 11b: Revision Class (From Lecture 6 to 10)
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Annotated Notes Lecture 11 Module 2 Summary So far
(61 pages)
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Lecture 12: Similar Matrices and Diagonalization
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Annotated Notes Lecture 12 Module 2 Diaognalisation
(100 pages)
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Lecture 13: Diagonalization Questions and Gram Schmidt Orthogonalization
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Annotated Notes Lecture 13 Module 2 SVD
(110 pages)
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Lecture 14: More on Singular Value Decomposition (SVD)
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Annotated Notes Lecture 14 Module 2 SVD
(68 pages)
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Lecture 15: Fundamental Subspaces with Singular Value Decomposition (SVD)
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Annotated Notes Lecture 15 Module 2 SVD
(58 pages)
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Practice Set 30 Questions on SVD
(67 pages)
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Lecture 16: Geometry of SVD and Practice Set 30 Questions Solution
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Annotated Notes Lecture 16 Module 2 SVD
(69 pages)
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Lecture 17: Practice Set 30 Questions Solution (Q11-Q30)
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Annotated Notes Lecture 17 Module 2 SVD More Question
(92 pages)
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Lecture 18: Orthogonal Projections
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Annotated Notes Lecture 18 Module 2 Projection Of a Vector
(58 pages)
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Lecture 19: Projection onto Subspace
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Annotated Notes Lecture 19 Module 2 Lecture 19 Projection onto Subspace
(57 pages)
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Lecture 20: Projection Matrix
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Annotated Notes Lecture 20 Module 2 Projection Matrix
(85 pages)
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Lecture 21: Weekly Quiz SVD Discussion
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Annotated Notes SVD Quiz
(71 pages)
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Lecture 22: Partition or Block Matrices Multiplication
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Annotated Notes Lecture 22 Module 2 Partition Matrix
(72 pages)
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Lecture 23: Block Matrices Other Operations
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Annotated Notes Lecture 23 Module 2 Partition Matrix all Operations
(113 pages)
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Lecture 24: Positive Definite Matrices
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Linear Algebra for GATE DA Module-2 Annotated Notes
(1 pages)
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Gilbert Strang Interview
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