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NPTEL

Linear Algebra

NPTEL and Indian Institute of Technology Kanpur via YouTube

Syllabus

Intro - Linear Algebra.
noc20-ma54-lec01_Notations, Motivation and Definition.
noc20-ma54-lec02_Matrix: Examples, Transpose and Addition.
noc20-ma54-lec03_Matrix Multiplication.
noc20-ma54-lec04_Matrix Product Recalled.
noc20-ma54-lec05_Matrix Product Continued.
noc20-ma54-lec06_Inverse of a Matrix.
noc20-ma54-lec07 - Introduction to System of Linear Equations.
noc20-ma54-lec08 - Some Initial Results on Linear Systems.
noc20-ma54-lec09 - Row Echelon Form (REF).
noc20-ma54-lec10 - LU Decomposition - Simplest Form.
noc20-ma54-lec11 - Elementary Matrices.
noc20-ma54-lec12 - Row Reduced Echelon Form (RREF).
noc20-ma54-lec13 - Row Reduced Echelon Form (RREF) Continued.
noc20-ma54-lec14 - RREF and Inverse.
noc20-ma54-lec15 - Rank of a matrix.
noc20-ma54-lec16 - Solution Set of a System of Linear Equations.
noc20-ma54-lec17 - System of n Linear Equations in n Unknowns.
noc20-ma54-lec18 - Determinant.
noc20-ma54-lec19 - Permutations and the Inverse of a Matrix.
noc20-ma54-lec20 - Inverse and the Cramer's Rule.
noc20-ma54-lec21 - Vector Spaces.
noc20-ma54-lec22 - Vector Subspaces and Linear Span.
noc20-ma54-lec23 - Linear Combination, Linear Independence and Dependence.
noc20-ma54-lec24 - Basic Results on Linear Independence.
noc20-ma54-lec25 - Results on Linear Independence Continued....
noc20-ma54-lec26 - Basis of a Finite Dimensional Vector Space.
noc20-ma54-lec27 - Fundamental Spaces associated with a Matrix.
noc20-ma54-lec28 - Rank - Nullity Theorem.
noc20-ma54-lec29 - Fundamental Theorem of Linear Algebra.
noc20-ma54-lec30 - Definition and Examples of Linear Transformations.
noc20-ma54-lec31 - Results on Linear Transformations.
noc20-ma54-lec32 - Rank-Nullity Theorem and Applications.
noc20-ma54-lec33 - Isomorphism of Vector Spaces.
noc20-ma54-lec34 - Ordered Basis of a Finite Dimensional Vector Space.
noc20-ma54-lec35 - Ordered Basis Continued.
noc20-ma54-lec36 - Matrix of a Linear transformation.
noc20-ma54-lec37 - Matrix of a Linear transformation Continued....
noc20-ma54-lec38 - Matrix of Linear Transformations Continued....
noc20-ma54-lec40 -Inner Product Space.
noc20-ma54-lec41 - Inner Product Continued.
noc20-ma54-lec42 - Cauchy Schwartz Inequality.
noc20-ma54-lec43 - Projection on a Vector.
noc20-ma54-lec44 - Results on Orthogonality.
noc20-ma54-lec45 - Results on Orthogonality.
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Taught by

IIT Kanpur July 2018

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