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Section 0: Introduction to Linear Algebra & Course Overview
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Lec1: Course Overview, WHY and WHAT of Linear Algebra, and Basics
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Understanding Vectors and Matrices
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Section 1: Vector Spaces (Optional for GATE CS)
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Vector Space, Subspace, Linear Independence and Basis
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Subspaces and Questions Practice
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Spans, Linear Independence and Basis
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Questions on Span and Linear Independence
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Practice Questions on Basis Dimensions
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Problem Discussion and Revision
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Doubt Class
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Problem Sheet
(6 pages)
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Section 2: Linear Maps/Transformations (Optional for GATE CS)
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Linear Maps and Fundamental Spaces
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Fundamental Subspaces and Linear Transformation as Matrices
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Practice Problems
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Practice Problems-2
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Common Mistakes with Null Space and Range Space
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Invertible Maps, Change of Basis
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Practice Problems
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Section 3: Systems of Linear Equations
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Introduction
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Gaussian Elimination
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Row Echelon Form and Gauss-Jordan Row Reduction Method
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Rank of a Matrix and its Significance
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Important Theorems and Practice Questions
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Section 4: Matrices, Types and Inverses
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Basics around Matrices
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Inverse of Matrix
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Section 5: Miscellaneous Topics
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Four Subspaces of A, Orthogonality and Duality
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Orthogonal Basis and Subspaces
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Projection Matrices
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Block Matrices, Trace and Determinants
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Doubt Session
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Revision
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1. Vector Spaces
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2. Vector Spaces and Linear Transformation
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3. Linear Transformation
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4. Linear Transformation Questions-1
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Section 6: Decompositions (SVD only for GATE DA)
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1. LU Decomposition
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2. LU Decomposition-2
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3. Eigen Vectors and Eigen Values
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4. Eigen Value Decomposition and Diagonalizability
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5. Quadtratic Forms
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6. Quadratic Forms-2
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7. SVD-1
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8. SVD-2
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9. Questions on SVD
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10. Important Questions on SVD
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11. Important Questions on SVD-2
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Launch your Graphy