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Details of MA2102 (Autumn 2020)

Level: 2 Type: Theory Credits: 3.0

Course CodeCourse NameInstructor(s)
MA2102 Linear Algebra I Somnath Basu

Syllabus



  1. Basic Material: System of linear equations, matrices, elementary row and column operations, echelon forms etc.


  2. Vector Spaces: Definition of a vector space, subspace, quotient space and their examples, linear independence, basis and dimension, rank-nullity theorem.


  3. Matrix and Determinant: Matrices as linear transformations, trace of a matrix, rank of a matrix, determinant of a matrix, properties of determinant, non-singularity, similar matrices, elementary matrices, special types of matrices, change of basis, dual spaces.


  4. Eigenvalues and Eigenvectors: Eigenvalues and eigenvectors of a matrix, characteristic polynomial, diagonalization.


  5. Inner Product Spaces: Orthogonal basis and the Gram-Schmidt orthogonalization process, orthogonal, unitary and Hermitian matrices, similarity and unitary similarity, Schur's triangularization theorem and the spectral theorem for normal matrices (statements only and if time permits)



References


  1. Axler, S., Linear Algebra Done Right, Springer-Verlag.

  2. Friedberg, S.H., Insel, A.J. and Spence, L.E., Linear Algebra, Prentice-Hall.

  4. Halmos P.R., Finite Dimensional Vector Spaces, Springer.

  5. Hoffman, K. and Kunze, R., Linear Algebra, Prentice-Hall.

  6. Horn, R. and Johnson, C.R., Matrix Analysis, Cambridge University Press.

  7. Kumeresan, S., Linear Algebra: Geometric Approach, Narosa Publishing

  8. Lang, S., Introduction to Linear Algebra, Springer-Verlag.

  9. Rao, A.R. and Bhimasankaran, P., Linear Algebra, Hindustan Book Agency.


Course Credit Options

Sl. No.ProgrammeSemester NoCourse Choice
1 IP 1 Not Allowed
2 IP 3 Not Allowed
3 IP 5 Not Allowed
4 MR 1 Not Allowed
5 MR 3 Not Allowed
6 MS ( Mathematical Sciences ) 3 Core
7 MS 5 Not Allowed
8 MS 7 Elective
9 MS 9 Not Allowed
10 RS 1 Not Allowed
11 RS 2 Not Allowed

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