Modules / Lectures

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Sl.No | Chapter Name | English |
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1 | Introduction to Algebraic Structures - Rings and Fields | PDF unavailable |

2 | Definition of Vector Spaces | PDF unavailable |

3 | Examples of Vector Spaces | PDF unavailable |

4 | Definition of subspaces | PDF unavailable |

5 | Examples of subspaces | PDF unavailable |

6 | Examples of subspaces (continued) | PDF unavailable |

7 | Sum of subspaces | PDF unavailable |

8 | System of linear equations | PDF unavailable |

9 | Gauss elimination | PDF unavailable |

10 | Generating system , linear independence and bases | PDF unavailable |

11 | Examples of a basis of a vector space | PDF unavailable |

12 | Review of univariate polynomials | PDF unavailable |

13 | Examples of univariate polynomials and rational functions | PDF unavailable |

14 | More examples of a basis of vector spaces | PDF unavailable |

15 | Vector spaces with finite generating system | PDF unavailable |

16 | Steinitzs exchange theorem and examples | Download Verified |

17 | Examples of finite dimensional vector spaces | Download Verified |

18 | Dimension formula and its examples | Download Verified |

19 | Existence of a basis | Download Verified |

20 | Existence of a basis (continued) | Download Verified |

21 | Existence of a basis [continued] | Download Verified |

22 | Introduction to Linear Maps | Download Verified |

23 | Examples of Linear Maps | Download Verified |

24 | Linear Maps and Bases | Download Verified |

25 | Pigeonhole principle in Linear Algebra | Download Verified |

26 | Interpolation and the rank theorem | Download Verified |

27 | Examples | Download Verified |

28 | Direct sums of vector spaces | Download Verified |

29 | Projections | Download Verified |

30 | Direct sum decomposition of a vector space | Download Verified |

31 | Dimension equality and examples | PDF unavailable |

32 | Dual spaces | PDF unavailable |

33 | Dual spaces (continued) | PDF unavailable |

34 | Quotient spaces | PDF unavailable |

35 | Homomorphism theorem of vector spaces | PDF unavailable |

36 | Isomorphism theorem of vector spaces | PDF unavailable |

37 | Matrix of a linear map | PDF unavailable |

38 | Matrix of a linear map (continued) | PDF unavailable |

39 | Matrix of a linear map [continued] | PDF unavailable |

40 | Change of bases | PDF unavailable |

41 | Computational rules for matrices | PDF unavailable |

42 | Rank of a matrix | PDF unavailable |

43 | Computation of the rank of a matrix | PDF unavailable |

44 | Elementary matrices | PDF unavailable |

45 | Elementary operations on matrices | PDF unavailable |

46 | LR decomposition | PDF unavailable |

47 | Elementary Divisor Theorem | PDF unavailable |

48 | Permutation groups | PDF unavailable |

49 | Canonical cycle decomposition of permutations | PDF unavailable |

50 | Signature of a permutation | PDF unavailable |

51 | Introduction to multilinear maps | PDF unavailable |

52 | Multilinear maps (continued) | PDF unavailable |

53 | Introduction to determinants | PDF unavailable |

54 | Determinants (continued) | PDF unavailable |

55 | Computational rules for determinants | PDF unavailable |

56 | Properties of determinants and adjoint of a matrix | PDF unavailable |

57 | Adjoint-determinant theorem | PDF unavailable |

58 | The determinant of a linear operator | PDF unavailable |

59 | Determinants and Volumes | PDF unavailable |

60 | Determinants and Volumes (continued) | PDF unavailable |

Sl.No | Language | Book link |
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1 | English | Not Available |

2 | Bengali | Not Available |

3 | Gujarati | Not Available |

4 | Hindi | Not Available |

5 | Kannada | Not Available |

6 | Malayalam | Not Available |

7 | Marathi | Not Available |

8 | Tamil | Not Available |

9 | Telugu | Not Available |