Rapidsol Algebra II (Pbi U)


The present book provides a comprehensive treatment of the concepts and topics by giving a vast variety of examples fully solved. The entire subject matter has been arranged in a systematic, graded, simple, lucid and exhaustive manner to meet the various needs of all types of learners. Each chapter begins with some definitions followed by theorems with complete proofs and solved problems so that the study leads to perfect clarity and understanding. A large number of notes and remarks have been added for a better understanding of the subject. Question Papers of previous years of various Universities examinations has been solved.


Vector spaces, Examples, Linear Dependence, Linear Combinations, Bases and Dimension, Subspaces, Quotient spaces, Direct Sum of vector spaces, Dimension of a direct sum, Dual of a vector space. Matrices and change of basis.

Linear transformation, Algebra of linear transformations, Matrices as linear mappings, Kernal and image, Rank and Nullity theorem, Singular and non-singular linear mappings, Isomorphism, Composition of linear mappings, Polynomials and linear operators, Square matrices as linear operators, matrix representation of a linear operator, Change of basis, characteristic and minimal polynomial for linear operators.


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