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Learn Linear Algebra and Master the Foundation of Machine Learning.
Instructor: Sachin Mittal (Ex - Amazon Applied Scientist, MTech IISc Bangalore)
Language: English
Validity Period: Lifetime
GO Classes Complete Discrete Mathematics and Engineering Mathematics Courses are FREE for all learners. Sign up and start learning.
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Features of the course:
One-Stop-Solution for your Complete Best GATE Preparation!!
1. Quality Content: No Rote-learning. No poor understadning. No By-hearting of formulas, tables or theorems. Understand everything with proofs-intuitions-ideas.
2. No Prerequisites: Every concept is taught from basics, without assuming any prior knowledge whatsoever.
3. Daily Homeworks: Practice material, with solutions, for Every Lecture to test your understanding of concepts of that respective lecture.
4. GATE PYQs Video Solution: Detailed Video Solution of All GATE Previous Years' Questions, with Complete Analysis of each question.
5. Summary Lectures: Short videos which summarises everything concept and detail of the course. Helps in quick revision.
6. Quality Practice Sets: Practice Sets from standard resources, with solutions, containing a lot of quality questions for practice.
7. Weekly Quizzes: Every week, there will be a Live Quiz, containing 15-20 questions, to evaluate your understanding of concepts taught in the previous week. The Quiz questions can be seen, solved even after tha live quiz is over.
8. Doubt Resolution: All of your doubts will be resolved directly by the faculty. There is a dedicated Telegram group for Enrolled Students of Goclasses where our faculties resolve students' Doubts. So, our students don't have to go anywhere else for asking doubts.
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 1A-1B (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(A|b) 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. CAYLEY-HAMILTON 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) | |||
Module-2 | |||
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 Module-2 HomeWork-1 (32 pages) | |||
LA for GATE DA Module-2 HomeWork-2 (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 Quiz-5 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 (Q11-Q30) | |||
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) | |||
Weekly Quiz SVD Discussion | |||
Annotated Notes SVD Quiz (71 pages) | |||
Gilbert Strang Interview |
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