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Quick Facts
| Medium Of Instructions | Mode Of Learning | Mode Of Delivery |
|---|---|---|
| English | Self Study | Video and Text Based |
Important dates
Course Commencement Date
Start Date : 20 Jan, 2025
End Date : 11 Apr, 2025
Enrollment Date
End Date : 27 Jan, 2025
Certificate Exam Date
Start Date : 26 Apr, 2025
Other
End Date : 14 Feb, 2025
Courses and Certificate Fees
| Fees Informations | Certificate Availability | Certificate Providing Authority |
|---|---|---|
| INR 1000 | yes | IIT Bombay |
The Syllabus
- Lecture 1: Why should we care about algebra?
- Lecture 2: Uses of linear algebra in different domains
- Lecture 3: Power of abstraction and geometric insights
- Lecture 4: Equivalent systems of linear equations
- Lecture 5: Row reduced form
- Lecture 6: Row reduced echelon form
- Lecture 7: Solving for Ax=0
- Lecture 8: Row rank of matrices
- Lecture 9: Groups and Abelian Groups
- Lecture 10: Rings, integral domains, and fields
- Lecture 11: Fields: Examples and properties
- Lecture 12: Vector Spaces
- Lecture 13: Examples of vector spaces
- Lecture 14: Subspaces
- Lecture 15: Examples of subspaces
- Lecture 16: Sum and intersection of subspaces
- Lecture 17: Span and linear independence
- Lecture 18: Generating set and basis
- Lecture 19: Properties of basis
- Lecture 20: Dimension of a vector space
- Lecture 21: Dimensions of special subspaces and properties
- Lecture 22: Co-ordinates and ordered basis
- Lecture 23: Row and column rank
- Lecture 24: Rank and nullity of matrices
- Lecture 25: Linear transformations and operators
- Lecture 26: Rank nullity theorem for linear transformations
- Lecture 27: Injective, surjective and bijective linear mappings
- Lecture 28: Isomorphism and their compositions
- Lecture 29: Linear transformations under change of basis
- Lecture 30: Linear functionals
- Lecture 31: Dual basis and dual maps
- Lecture 32: Annihilators, double duals
- Lecture 33: Products of vector spaces
- Lecture 34: Quotient spaces
- Lecture 35: Quotient maps
- Lecture 36: First isomorphism theorem
- Lecture 37: Inner product spaces
- Lecture 38: Examples of inner products
- Lecture 39: Cauchy Schwarz and triangle inequalities
- Lecture 40: Some results and applications of inner products (in solving Ax=b)
- Lecture 41: Gram-Schmidt orthonormalization
- Lecture 42: Best approximation of a vector in a subspace
- Lecture 43: Orthogonal complements of subspaces and their properties
- Lecture 44: Orthogonal projection map and its properties
- Lecture 45: “Best” solution for Ax=b
- Lecture 46: Applications of “best” solution
- Lecture 47: Adjoint operators on inner product spaces
- Lecture 48: Miscellaneous results on inner products and inner product spaces, and their applications (e.g. Haar wavelets, Fourier series)
- Lecture 49: Solutions of linear second order differential equations and phase portraits
- Lecture 50: Eigenvalues and eigen vectors
- Lecture 51: Diagonalizability for self-adjoint operators
- Lecture 52: Linear independence of eigen vectors and diagonalizability, evaluation of matrix functions
- Lecture 53: Algebraic and geometric multiplicities
- Lecture 54: Decomposition of a vector space into sums and direct sums of suitable subspaces
- Lecture 55: Equivalent conditions for diagonalizability
- Lecture 56: A-invariant subspaces: definition and examples
- Lecture 57: Polynomials and their ideals
- Lecture 58: Minimal polynomial
- Lecture 59: Minimal polynomial and characteristic polynomial
- Lecture 60: Further properties of minimal polynomial
- Lecture 61: Bezout’s identity for polynomials
- Lecture 62: Application of Bezout’s identity to coprime factors of minimal polynomial
- Lecture 63: Recipe for best representation of non-diagonalizable linear operators
- Lecture 64: Jordan canonical form
- Lecture 65: Proof for Jordan canonical form
- Lecture 66: Proof of Cayley Hamilton theorem
- Lecture 67: Application of linear algebra to algebraic graph theory
- Lecture 68: Properties of graph Laplacian matrix: Fiedler eigenvalue
- Lecture 69: Consensus problem
- Lecture 70: Solution of the agreement protocol
- Lecture 71: Applications to opinion dynamics
- Lecture 72: Further applications of linear algebra to multi-agent systems
Instructors
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