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Linear Algebra (Prof. Arbind Kumar Lal, IIT Kanpur). Instructor: Prof. Arbind Kumar Lal, Department of Mathematics and Statistics, IIT Kanpur.
FREE
This course includes
Hours of videos
1833 years, 1 month
Units & Quizzes
66
Unlimited Lifetime access
Access on mobile app
Certificate of Completion
The course will assume basic knowledge of class XII algebra and a familiarity with calculus. Even though the course will start with defining matrices and operations associated with it. This will lead to the study of a system of linear equations, elementary matrices, invertible matrices, the row-reduced echelon form of a matrix and a few equivalent conditions for a square matrix to be invertible. From here, we will go into the axiomatic definition of vector spaces over real and complex numbers, try to understand linear combination, linear span, linear independence and linear dependence and hopefully understand the basis of a finite dimensional vector space. (from nptel.ac.in)
Course Currilcum
- Lecture 01 – Notations, Motivation and Definition Unlimited
- Lecture 02 – Matrix: Examples, Transpose and Addition Unlimited
- Lecture 03 – Matrix Multiplication Unlimited
- Lecture 04 – Matrix Product Recalled Unlimited
- Lecture 05 – Matrix Product (cont.) Unlimited
- Lecture 06 – Inverse of a Matrix Unlimited
- Lecture 07 – Introduction to System of Linear Equations Unlimited
- Lecture 08 – Some Initial Results on Linear Systems Unlimited
- Lecture 09 – Row Echelon Form (REF) Unlimited
- Lecture 10 – LU Decomposition – Simplest Form Unlimited
- Lecture 11 – Elementary Matrices Unlimited
- Lecture 12 – Row Reduced Echelon Form (RREF) Unlimited
- Lecture 13 – Row Reduced Echelon Form (cont.) Unlimited
- Lecture 14 – RREF and Inverse Unlimited
- Lecture 15 – Rank of a Matrix Unlimited
- Lecture 16 – Solution Set of a System of Linear Equations Unlimited
- Lecture 17 – System of n Linear Equations in n Unknowns Unlimited
- Lecture 18 – Determinant Unlimited
- Lecture 19 – Permutations and the Inverse of a Matrix Unlimited
- Lecture 20 – Inverse and the Cramer’s Rule Unlimited
- Lecture 21 – Vector Spaces Unlimited
- Lecture 22 – Vector Subspaces and Linear Span Unlimited
- Lecture 23 – Linear Combination, Linear Independence and Dependence Unlimited
- Lecture 24 – Basic Results on Linear Independence Unlimited
- Lecture 25 – Results on Linear Independence (cont.) Unlimited
- Lecture 26 – Basis of a Finite Dimensional Vector Space Unlimited
- Lecture 27 – Fundamental Spaces Associated with a Matrix Unlimited
- Lecture 28 – Rank-Nullity Theorem Unlimited
- Lecture 29 – Fundamental Theorem of Linear Algebra Unlimited
- Lecture 30 – Definition and Examples of Linear Transformations Unlimited
- Lecture 31 – Results on Linear Transformations Unlimited
- Lecture 32 – Rank-Nullity Theorem and Applications Unlimited
- Lecture 33 – Isomorphism of Vector Spaces Unlimited
- Lecture 34 – Ordered Basis of a Finite Dimensional Vector Space Unlimited
- Lecture 35 – Ordered Basis of a Finite Dimensional Vector Space (cont.) Unlimited
- Lecture 36 – Matrix of a Linear Transformation Unlimited
- Lecture 37 – Matrix of a Linear Transformation (cont.) Unlimited
- Lecture 38 – Matrix of Linear Transformations (cont.) Unlimited
- Lecture 39 – Similarity of Matrices Unlimited
- Lecture 40 – Inner Product Space Unlimited
- Lecture 41 – Inner Product (cont.) Unlimited
- Lecture 42 – Cauchy Schwarz Inequality Unlimited
- Lecture 43 – Projection on a Vector Unlimited
- Lecture 44 – Results on Orthogonality Unlimited
- Lecture 45 – Results on Orthogonality (cont.) Unlimited
- Lecture 46 – Gram-Schmidt Orthogonalization Process Unlimited
- Lecture 47 – Orthogonal Projections Unlimited
- Lecture 48 – Gram-Schmidt Process: Applications Unlimited
- Lecture 49 – Examples and Applications on QR-Decomposition Unlimited
- Lecture 50 – Recapitulate Ideas on Inner Product Spaces Unlimited
- Lecture 51 – Motivation on Eigenvalues and Eigenvectors Unlimited
- Lecture 52 – Examples and Introduction to Eigenvalues and Eigenvectors Unlimited
- Lecture 53 – Results on Eigenvalues and Eigenvectors Unlimited
- Lecture 54 – Results on Eigenvalues and Eigenvectors (cont.) Unlimited
- Lecture 55 – Results on Eigenvalues and Eigenvectors (cont.) Unlimited
- Lecture 56 – Diagonalizability Unlimited
- Lecture 57 – Diagonalizability (cont.) Unlimited
- Lecture 58 – Schur’s Unitary Triangularization (SUT) Unlimited
- Lecture 59 – Applications of Schur’s Unitary Triangularization Unlimited
- Lecture 60 – Spectral Theorem for Hermitian Matrices Unlimited
- Lecture 61 – Cayley Hamilton Theorem Unlimited
- Lecture 62 – Quadratic Forms Unlimited
- Lecture 63 – Sylvester’s Law of Inertia Unlimited
- Lecture 64 – Applications of Quadratic Forms to Analytic Geometry Unlimited
- Lecture 65 – Examples of Conics and Quartics Unlimited
- Lecture 66 – Singular Value Decomposition (SVD) Unlimited
