Course Archives Theoretical Statistics and Mathematics Unit
Course: Linear Algebra I
Instructor: Anita Naolekar
Level: Undergraduate
Time: Currently offered
Past Exams


Homogeneous and non-homogeneous systems of linear equations, condition for consistency, solution set as a translate of a subspace.
Vector spaces, subspaces, linear independence, span, basis and dimension, sum and intersection of subspaces, direct sum, complement and projection.
Linear transformation and its matrix with respect to a pair of bases, properties of matrix operations, use of partitioned matrices.
Column space and row space, rank of a matrix, nullity, rank of AA*.
g-inverse and its elementary properties, left inverse, right inverse and inverse, inverse of a partitioned matrix, lower and upper bounds for rank of a product, rankfactorization of a matrix, rank of a sum. Elementary operations and elementary matrices, Echelon form, Normal form, Hermite canonical form and their use in solving linear equations and in finding inverse or g-inverse. LDU-decomposition.

Note: The field of scalars should be assumed to be subfields of complex numbers, i.e., subsets closed under addition, subtraction, multiplication and division by a nonzero number. The main examples to be considered should be the field of real, complex or rational numbers.

Reference Texts:

(a) C. R. Rao: Linear Statistical Inference and its Applications.
(b) A. Ramachandra Rao and P. Bhimasankaram: Linear Algebra.
(c) K. Hoffman and R. Kunze: Linear Algebra.
(d) F. E. Hohn: Elementary Matrix Algebra.
(e) P. R. Halmos: Finite Dimensional Vector Spaces.
(f) S. Axler: Linear Algebra Done Right!
(g) H. Helson: Linear Algebra.
(h) R Bapat: Linear Algebra and Linear Models.
(i) R. A. Horn and C. R. Johnson: Matrix Analysis.
(j) M. Artin: Algebra.

Midterm marks
Assignments marks
Final Exam marks
Total 100 marks

Top of the page

Past Exams
23.pdf 24.pdf
22.pdf 23.pdf 24.pdf
Supplementary and Back Paper
22.pdf 23.pdf 24.pdf

Top of the page

[ Semester Schedule ][ Statmath Unit ] [Indian Statistical Institute]