University of Madras - Syllabus of Bachelor of Science (BSc) Mathematics - Semester IV - Allied - Mathematics for Statistics II

UNIVERSITY OF MADRAS

B.Sc. DEGREE COURSE IN MATHEMATICS

SEMESTER SYSTEM WITH CREDITS

(Effective from the Academic Year 2003-2004)

SYLLABUS

Semester IV - Allied - Mathematics for Statistics II

Duration of Examination: 3 hrs

Maximum Marks: 100

Credits: 4

Matrix theory - definition and types of matrices, Scalar, Elementary, Symmetric, Skew symmetric, Hermitian, Skew - Hermitian, independent and unitary matrices - algebraic operations on matrices and their properties - elementary transformations of matrices - determinant of matrix - definition of a row rank - column rank and rank of a matrix - determination of a rank of a matrix.

Inverse of a square matrix - computation of the inverse of the square matrix - solution of linear equations - Homogenous and non-homogeneous systems of equations - solutions space - consistency and general solutions Cramer's Rule and matrix methods of solving system equations - numerical examples, characteristic equations - root and vectors of a square matrix - left and right eigen vectors - Cayley - Hamilton theorem - Quadratic forms, definite, semi definite and indefinite quadraticforms, Sylvester's law of inertia.

Vector spaces - definition of a vector space with real scalars - linear combination of vectors - linear dependence and independence - definition of a subspace and its characterizations - orthogonal basis and Gram - schmidt orthogonalizations process - examples in Rn.

Books for Study & Reference:

Searle, S.R. (1982) : Matrix algebra useful for Statistics, John Wiley and Sons.

Vasistha, A.R. : Matrices, Krishna Prakasam Mandir.

Shanthinarayanan (1959) : A text book of Matrices, S. Chand & Co.

Graybill, F.A. (1983) : Matrices with applications in Statistics, 2

^{nd} ed. Wadsworth.

Bellman, R. (1970) : Introduction to Matrix analysis.

Hobn, F.E. (1971) : Elementary Matrix Algebra. Amerind Pub. Coy. Pvt. Ltd.