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Introduction to Abstract and Linear Algebra

Introduction to Abstract and Linear Algebra. Instructor: Dr. Sourav Mukhopadhyay, Department of Mathematics, IIT Kharagpur. Abstract and Linear Algebra are applicable to every discipline, be it engineering and technology, economics or social sciences. It is essential for the students to get acquainted with the subject of Abstract and Linear Algebra at an early stage. The present course has been designed to introduce the subject to undergraduate/postgraduate students in science and engineering. The course contains a good introduction to each topic and an advance treatment of theory at a fairly understandable level to the students at this stage. (from nptel.ac.in)

Lecture 31 - Rank of a Matrix


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Lecture 01 - Set Theory
Lecture 02 - Set Operations
Lecture 03 - Set Operations (cont.)
Lecture 04 - Set of Sets
Lecture 05 - Binary Relation
Lecture 06 - Equivalence Relation
Lecture 07 - Mapping
Lecture 08 - Permutation
Lecture 09 - Binary Composition
Lecture 10 - Groupoid
Lecture 11 - Group
Lecture 12 - Order of an Element
Lecture 13 - Subgroup
Lecture 14 - Cyclic Group
Lecture 15 - Subgroup Operations
Lecture 16 - Left Cosets
Lecture 17 - Right Cosets
Lecture 18 - Normal Subgroup
Lecture 19 - Rings
Lecture 20 - Field
Lecture 21 - Vector Spaces
Lecture 22 - Subspaces
Lecture 23 - Linear Span
Lecture 24 - Basis of a Vector Space
Lecture 25 - Dimension of a Vector Space
Lecture 26 - Complement of Subspace
Lecture 27 - Linear Transformation
Lecture 28 - Linear Transformation (cont.)
Lecture 29 - More on Linear Mapping
Lecture 30 - Linear Space
Lecture 31 - Rank of a Matrix
Lecture 32 - Rank of a Matrix (cont.)
Lecture 33 - System of Linear Equations
Lecture 34 - Row Rank and Column Rank
Lecture 35 - Eigenvalue of a Matrix
Lecture 36 - Eigenvector
Lecture 37 - Geometric Multiplicity
Lecture 38 - More on Eigenvalue
Lecture 39 - Similar Matrices
Lecture 40 - Diagonalisable