TB Abstract Algebra |Edition-2 | Pages-464 | Code-1393 |Concept+ Theorems/Derivation + Solved Numericals + Practice Exercise | Text Book

by A.R. Vasishtha

SYLLABUS- ABSTRACT ALGEBRA, Section-ARings and Introduction to rings, Integral domains and fields, Characteristicof a ring, Ring homomorphism, Ideals and quotient rings, Field of quotients of anintegral domain, Euclidean rings. Polynomial rings, Polynomials over the rationalfield, Eisenstein’s criteria, Unique factorization domain.Section-BVector Definition and examples of vector spaces, Subspaces, Sum and directsum of subspace, Linear span, Linear dependence, Independence and their basicproperties, Basis Dimension, Existence of complementary subspace of a subspace of afinite dimensional vector space, Dimensions of sums of subspaces, Quotient spaceand its dimension.Linear transformations and their representations as matrices, The algebra of lineartransformations, The rank — nullity theorem, Change of basis. Dual space, Bidualspace end natural isomorphism.Application of matrices to a system of linear (both homogeneous and non-homogeneous)equations, Theorems on consistency of a system of linear equations,The characteristic equation of a matrix, Eigen values and eigen vectors, Cayley-Hamilton theorem and its use in finding inverse of a matrix, Diagonalisation ofsquare matrices with distinct eigen values.

Kindle Edition

Published May 23, 2021