2
Applied Linear Algebra. Instructor: Prof. Andrew Thangaraj, Department of Electrical Engineering, IIT Madras.
FREE
This course includes
Hours of videos
1305 years, 5 months
Units & Quizzes
47
Unlimited Lifetime access
Access on mobile app
Certificate of Completion
This course introduces the fundamentals of vector spaces, inner products, linear transformations, and eigenspaces to electrical engineering students. (from nptel.ac.in)
Course Currilcum
- 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
