Linear Algebra


Objective of the course: Solving systems of linear equations, Understanding vector spaces, linear transformations, eigenvalue, eigenvector, generalized notion of angle, distance, and length, diagonalization and orthogonalization.

Outcome of the course: To able to solve systems of linear equations, work within vector spaces, to manipulate matrices and to do matrix algebra.

Course outlines:
Unit-I: System of linear equation, Gauss elimination method, Elementary matrices, Invertible matrices, Gauss-Jordon method for finding inverse of a matrix, Determinant, Cramer's rule, Vector spaces, Linearly independence and independence, Basis, Dimension.

Unit-II: Linear transformation, Representation of linear maps by matrices, Rank-Nullity theorem, Rank of a matrix, Row and column spaces, Solution space of a system of homogeneous and non-homogeneous equations, Inner product space, Cauchy-Schwartz inequality, Orthogonal basis.

Unit-III: Grahm-Schmidt orthogonalization process, Orthogonal projection, Eigen value, eigenvector, Cayley-Hamilton theorem, Diagonalizability and minimal polynomial, Spectral theorem.

Unit-IV: Positive, negative and semi definite matrices. Decomposition of the matrix in terms of projections, Strategy for choosing the basis for the four fundamental subspaces, Least square solutions and fittings, Singular values, Primary decomposition theorem, Jordan canonical form.

Text book: Gilbert Strang, Linear Algebra, Cambridge Press.

Reference books:
1: K. Hoffman and R. Kunze, Linear Algebra, Pearson.
2: S. Kumaresan, Linear algebra - A Geometric approach, Prentice Hall of India.
3: S. Lang, Introduction to Linear Algebra, Springer.


Lecture schedule     Tutorial schedule

Seating plan during lectures     Seating plan during tutorials


Tutorial discription

Content Problem set
Group, elementary matrix, row reduced echelon form, Gauss Jordan method Problem set 1
Determinant, Vector spaces, Subspace, Basis, Dimension Problem set 2
Linear Map and its matrix representation Problem set 3
Inner product space Problem set 4
Eigenvalues, Eigenvectors Problem set 5
Positive and Negative definite matrices, Jordan cannonical form, Singular value decomposition Problem set 6


Assesment/Evaluation discription

Exam Tentative Marking Scheme
Quiz 1 (C1) PDF
Quiz 2 (C1) PDF
Review Test (C1) PDF
Quiz 1(C2) PDF
Review Test (C2) PDF







Marks of Linear Algebra: July - December, 2019

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Attendance Record of Linear Algebra: July - December, 2019

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