Precize Algebra II (Pbi U)


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The book is strictly in accordance with the latest syllabus of the PUNJABI UNIVERSITY, PATIALA. The entire subject matter has been arranged in a systematic, graded, simple, lucid and exhaustive manner. Each chapter begins with some definitions followed by theorems with complete proofs and solved problems. A large number of notes and remarks have been added for a better understanding of the subject. Well-planned and exhaustive exercises have been given in each chapter.

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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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