Theory

Syllabus( For theory)(B.Sc. in Statistics) 

Unit-1:

• Definition of vectors, operation of vectors (angle, distance etc.). Vector spaces, Subspaces, sum of subspaces, Span of a set, Linear dependence and independence, dimension and basis, dimension theorem. Extension of basis. Orthogonal vectors, Gram-Schmidt Orthogonalization. 

Unit-2:

• Algebra of matrices. Linear transformation. Elementary matrices and their uses, theorems related to triangular, symmetric and skew symmetric matrices, Hermitian and skew Hermitian matrices, Idempotent matrices, Orthogonal matrices. 

Unit-3: 

• Determinant of Matrices: Definition, properties and applications of determinants for 3rd and higher orders, evaluation of determinants, using transformations. Symmetric and Skew symmetric determinants, product of determinants. Use of determinants in solution to the system of linear equations. Adjoint and inverse of a matrix and related properties. Singular and nonsingular matrices and their properties. Conditions for consistency, uniqueness, infinite solutions, solution sets of linear equations, linear independence, Applications of linear equations. 

Unit-4:

• Rank of a matrix, row-rank, column-rank, standard theorems on ranks, rank of the sum and the product of two matrices. Partitioning of matrices and simple properties. Characteristic roots and Characteristic vectors, Properties of characteristic roots, Quadratic forms: Classification & Canonical reduction. Linear orthogonal transformation, Matrix diagonalization.