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Applied Linear Algebra. Instructor: Prof. Andrew Thangaraj, Department of Electrical Engineering, IIT Madras.

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September 23, 2023

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September 23, 2023

Duration:

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FREE

This course includes:

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Description

Applied Linear Algebra. Instructor: Prof. Andrew Thangaraj, Department of Electrical Engineering, IIT Madras.

This course introduces the fundamentals of vector spaces, inner products, linear transformations, and eigenspaces to electrical engineering students. (from nptel.ac.in)

Course Curriculum

  • Lecture 01 – Vector Spaces: Introduction Unlimited
  • Lecture 02 – Linear Combinations and Span Unlimited
  • Lecture 03 – Subspaces, Linear Dependence and Independence Unlimited
  • Lecture 04 – Basis and Dimension Unlimited
  • Lecture 05 – Sums, Direct Sums and Gaussian Elimination Unlimited
  • Lecture 06 – Linear Maps and Matrices Unlimited
  • Lecture 07 – Null Space, Range, Fundamental Theorem of Linear Maps Unlimited
  • Lecture 08 – Column Space, Null Space and Rank of a Matrix Unlimited
  • Lecture 09 – Algebraic Operations on Linear Maps Unlimited
  • Lecture 10 – Invertible Maps, Isomorphism, Operators Unlimited
  • Lecture 11 – Solving Linear Equations Unlimited
  • Lecture 12 – Elementary Row Operations Unlimited
  • Lecture 13 – Translates of a Subspace, Quotient Spaces Unlimited
  • Lecture 14 – Row Space and Rank of a Matrix Unlimited
  • Lecture 15 – Determinants Unlimited
  • Lecture 16 – Coordinates and Linear Maps under a Change of Basis Unlimited
  • Lecture 17 – Simplifying Matrices of Linear Maps by Choice of Basis Unlimited
  • Lecture 18 – Polynomials and Roots Unlimited
  • Lecture 19 – Invariant Subspaces, Eigenvalues, Eigenvectors Unlimited
  • Lecture 20 – More on Eigenvalues, Eigenvectors, Diagonalization Unlimited
  • Lecture 21 – Eigenvalues, Eigenvectors and Upper Triangularization Unlimited
  • Lecture 22 – Properties of Eigenvalues Unlimited
  • Lecture 23 – Linear State Space Equations and System Stability Unlimited
  • Lecture 24 – Discrete-Time Linear Systems and Discrete Fourier Transforms Unlimited
  • Lecture 25 – Sequences and Counting Paths in Graphs Unlimited
  • Lecture 26 – PageRank Algorithm Unlimited
  • Lecture 27 – Dot Product and Length in Cn, Inner Product and Norm in V over F Unlimited
  • Lecture 28 – Orthonormal Basis and Gram-Schmidt Orthogonalization Unlimited
  • Lecture 29 – Linear Functions, Orthogonal Complements Unlimited
  • Lecture 30 – Orthogonal Projection Unlimited
  • Lecture 31 – Projection and Distance from a Subspace Unlimited
  • Lecture 32 – Linear Equations, Least Squares Solutions and Linear Regression Unlimited
  • Lecture 33 – Minimum Mean Squared Error Estimation Unlimited
  • Lecture 34 – Adjoint of a Linear Map Unlimited
  • Lecture 35 – Properties of Adjoint of a Linear Map Unlimited
  • Lecture 36 – Adjoint of an Operator and Operator-Adjoint Product Unlimited
  • Lecture 37 – Self-Adjoint Operator Unlimited
  • Lecture 38 – Normal Operators Unlimited
  • Lecture 39 – Complex Spectral Theorem Unlimited
  • Lecture 40 – Real Spectral Theorem Unlimited
  • Lecture 41 – Positive Operators Unlimited
  • Lecture 42 – Quadratic Forms, Matrix Norms and Optimization Unlimited
  • Lecture 43 – Isometries Unlimited
  • Lecture 44 – Classification of Operators Unlimited
  • Lecture 45 – Singular Values and Vectors of a Linear Map Unlimited
  • Lecture 46 – Singular Value Decomposition Unlimited
  • Lecture 47 – Polar Decomposition and Some Applications of SVD Unlimited

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