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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 14 - Cyclic Group

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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