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Created by:
Last updated:
September 23, 2023
Duration:
EXPIRED
FREE
This course includes:
EXPIRED
Badge on Completion
Certificate of completion
EXPIRED
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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