
Module 1: Basics of Linear Algebra




Lecture 1A  Why Study Linear Algebra
22:00




Lecture 1B  Linear Algebra for GATE & Interviews
14:00




Annotated Notes  Lecture 1A1B
(32 pages)




Lecture 1C  Linearly Independent and Linearly Dependent
75:00




Annotated Notes  Lecture 1C
(92 pages)




Lecture 2A  Filling the Space Part 1
44:00




Lecture 2B  Filling the Space Part 2
28:00




Lecture 2C  Summary so far
12:00




Lecture 2D  Multiplying a Matrix & a Vector
26:00




Annotated Notes  Lecture 2
(103 pages)




Homework 1  Linear Dependence & Independence
(12 pages)




Live Session 1  Homework 1 Discussion




Annotated Notes  Live Session 1
(20 pages)




Lecture 3A  Why Solve System Of Linear Equations
22:00




Lecture 3B  Writing as Ax=b, Geometric Interpretation and Possible Solutions
24:00




Lecture 3C  Understanding Ax=b intuitively
44:00




Lecture 3 Annotated Notes
(74 pages)




4a. Multiplying 2 Matrices  My Walmart Interview Question
18:00




4b. GATE 2016 Question
16:00




4c. GATE 2014 Question
14:00




4d. Two conceptual questions
28:00




4e. Linear Combination of Independent vectors is unique
28:00




4f. GATE 2017 Question
4:00




Lecture 4 Annotated Notes
(76 pages)




Homework 2
(20 pages)




5a. Echelon Form and Pivot Columns
37:00




5b. Gaussian Elimination
26:00




Live Session 2
94:00




Live Session 2 Annotated Notes
(48 pages)




5c. Rank  GATE 1994 Question  Rank Nullity Theorem
11:00




5d. Finally Solving Ax=b  Five Different Questions
33:00




5e. More than one free variable in 𝐴𝑥=0 solution
32:00




Lecture 5 Annotated Notes
(125 pages)




Recording  Live Session 3
60:00




Live Session 3




Live Session 3 Annotated Notes
(18 pages)




6a. GATE 2021 Question  Free variables in Non homogeneous
19:00




6b. Solutions based on Rank(A) and Rank(Ab)
18:00




6c. Few Questions related to rank(A) and Number of solutions
8:00




6d. [OPTIONAL] Linearly Independent Columns with Gaussian Elimination
24:00




6e. [Optional] Row Reduced Echelon Form
28:00




Lecture 6 Annotated Notes
(74 pages)




Homework Questions Set 2
(20 pages)




Lecture 7 Determinant
100:00




Lecture 7b Inverse of a Matrix




Lecture 7c. Crammer's rule
26:00




Lecture 7 Annotated Notes
(149 pages)




Lecture 8a. Introduction to Eigenvalues and Eigenvectors
23:00




Lecture 8b. Characterstic Equation
15:00




Lecture 8c. Solving for Eigenvalues and Eigenvectors
22:00




Lecture 8 Annotated Notes
(45 pages)




Lecture 9a. Linearly Independent eigen vectors with repeating eigenvalues
21:00




Lecture 9b. Three Different Examples With Repeating Lambda
30:00




Lecture 9c. Symmetric Matrices has n LI Eigen Vectors
12:00




Lecture 9d. Two Magical Properties
12:00




Lecture 9 Annotated Notes
(95 pages)




(New) Practice Questions based on Concepts covered upto lecture 4F




Annotated Notes Practice Questions based on Concepts covered upto lecture 4F
(79 pages)




(New) Practice Questions based on Concepts covered upto lecture 4F  Part2




Annotated Notes Practice Questions based on Concepts covered upto lecture 4F Part2
(82 pages)




10a. Rank and Eigen Values
22:00




10b. Examples on Rank and Eigen Values
15:00




10c. CAYLEYHAMILTON THEOREM
16:00




10d. Eigen Values of AB and BA
32:00




10e. Eigen Values of Powers of A
17:00




Lecture 10 Annotated Notes
(99 pages)




Lecture 11a. LU Decomposition
25:00




Lecture 11b. Type Of Matrices
84:00




Lecture 11 Annotated Notes
(80 pages)




Weekly Quiz 3 GATE 2025 Solution




Annotated Notes Weekly Quiz 3 Linear Algebra
(64 pages)



Module2




Lecture 1: Introduction to Vector Spaces, Subspaces, Basis, and Span




Annotated Notes Lecture 1 Module 2 Definition of Vector Spaces and SubSpaces
(86 pages)




Lecture 2: Basis, Span, Subspaces of Matrix A (Column and Null Space)




Annotated Notes Lecture 2 Module 2 Basis Span and Dim of Space
(97 pages)




Lecture 3: Subspaces of Matrix A (Column and Null Space)




Annotated Notes Lecture 3 Module 2 Col and Null Space
(81 pages)




Lecture 4: Subspaces of Matrix A (Row and Left Null Space)




Annotated Notes Lecture 4 Module 2 Row and Left Null Space
(75 pages)




LA for GATE DA Module2 HomeWork1
(32 pages)




LA for GATE DA Module2 HomeWork2
(27 pages)




Lecture 5: Four Fundamental Subspaces




Annotated Notes Lecture 5 Module 2 Four Fundamental Subspaces
(71 pages)




Lecture 6: Change of Basis




Annotated Notes Lecture 6 Module 2 Change of Basis
(77 pages)




Lecture 7: Linear Transformation




Annotated Notes Lecture 7 Module 2 Linear Transformation
(81 pages)




Lecture 8: More on Linear Transformation




Annotated Notes Lecture 8 Module 2 More on Linear Transformation
(186 pages)




Lecture 9: Linear Transformation w.r.t. arbitrary bases




Annotated Notes Lecture 9 Module 2 Linear Transformation in different bases
(105 pages)




Lecture 10: Questions on Change of Basis and Linear Transformation




Annotated Notes Lecture 10 Module 2 Questions on Linear Transformation and change of bases
(58 pages)




Weekly Quiz
(34 pages)




Weekly Quiz5 Solution Discussion




Lecture 11a: Revision Class (From Lecture 1 to 5)




Lecture 11b: Revision Class (From Lecture 6 to 10)




Annotated Notes Lecture 11 Module 2 Summary So far
(61 pages)




Lecture 12: Similar Matrices and Diagonalization




Annotated Notes Lecture 12 Module 2 Diaognalisation
(100 pages)




Lecture 13: Diagonalization Questions and Gram Schmidt Orthogonalization




Annotated Notes Lecture 13 Module 2 SVD
(110 pages)




Lecture 14: More on Singular Value Decomposition (SVD)




Annotated Notes Lecture 14 Module 2 SVD
(68 pages)




Lecture 15: Fundamental Subspaces with Singular Value Decomposition (SVD)




Annotated Notes Lecture 15 Module 2 SVD
(58 pages)




Practice Set 30 Questions on SVD
(67 pages)




Lecture 16: Geometry of SVD and Practice Set 30 Questions Solution




Annotated Notes Lecture 16 Module 2 SVD
(69 pages)




Lecture 17: Practice Set 30 Questions Solution (Q11Q30)




Annotated Notes Lecture 17 Module 2 SVD More Question
(92 pages)




Lecture 18: Orthogonal Projections




Annotated Notes Lecture 18 Module 2 Projection Of a Vector
(58 pages)




Lecture 19: Projection onto Subspace




Annotated Notes Lecture 19 Module 2 Lecture 19 Projection onto Subspace
(57 pages)




Lecture 20: Projection Matrix




Annotated Notes Lecture 20 Module 2 Projection Matrix
(85 pages)




Lecture 21: Weekly Quiz SVD Discussion




Annotated Notes SVD Quiz
(71 pages)




Lecture 22: Partition or Block Matrices Multiplication




Annotated Notes Lecture 22 Module 2 Partition Matrix
(72 pages)




Lecture 23: Block Matrices Other Operations




Annotated Notes Lecture 23 Module 2 Partition Matrix all Operations
(113 pages)




Linear Algebra for GATE DA Module2 Annotated Notes
(1 pages)



Gilbert Strang Interview

