MA3104 : Linear Algebra II (Autumn 2020) | Academic Portal of IISER Kolkata

Details of MA3104 (Autumn 2020)

Level: 3

Type: Theory

Credits: 4.0

Course Code	Course Name	Instructor(s)
MA3104	Linear Algebra II	Subrata Shyam Roy

Syllabus
Eigenvalues: Annihilating polynomials, minimal polynomials, invariant subspaces, simultaneous diagonalization and triangularization, direct sum decompositions, primary decomposition theorem. Canonical Forms: Cyclic decompositions and the rational form, Jordan canonical form, computation of invariant factors. Matrix Decomposition: Orthogonal, unitary and Hermitian matrices, unitary similarity, Schur's triangularization theorem, spectral theorem for normal matrices, positive definite matrices, polar decomposition, singular value decomposition. Bilinearity: Bilinear maps, tensors and tensor product with emphasize on inner product space. Exterior Forms: Quadratic forms, bilinear forms, symmetric and alternating forms, determinant function and uniqueness of determinant.

Syllabus

Eigenvalues: Annihilating polynomials, minimal polynomials, invariant subspaces, simultaneous diagonalization and triangularization, direct sum decompositions, primary decomposition theorem.
Canonical Forms: Cyclic decompositions and the rational form, Jordan canonical form, computation of invariant factors.
Matrix Decomposition: Orthogonal, unitary and Hermitian matrices, unitary similarity, Schur's triangularization theorem, spectral theorem for normal matrices, positive definite matrices, polar decomposition, singular value decomposition.
Bilinearity: Bilinear maps, tensors and tensor product with emphasize on inner product space.
Exterior Forms: Quadratic forms, bilinear forms, symmetric and alternating forms, determinant function and uniqueness of determinant.

Prerequisite
Linear Algebra I (MA2102)

References
Axler, S., Linear Algebra Done Right, Springer-Verlag. Friedberg, S.H., Insel, A.J. and Spence, L.E., Linear Algebra, Prentice-Hall. Horn, R. and Johnson, C.R., Matrix Analysis, Cambridge University Press. Hoffman, K. and Kunze, R., Linear Algebra (2nd Edition), Prentice-Hall. Lang, S., Introduction to Linear Algebra (2nd Edition), Springer-Verlag. Lax, P.D., Linear Algebra and Its Applications, Wiley. Rao, A.R. and Bhimasankaran, P., Linear Algebra (2nd Edition), Hindustan Book Agency. Roman, S., Advanced Linear Algebra, Springer. Shafarevich, I.R. and Remizov, A.O., Linear Algebra and Geometry, Springer.

References

Rao, A.R. and Bhimasankaran, P., Linear Algebra (2nd Edition), Hindustan Book Agency.

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