Rapidsol Linear Algebra (PU)


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. 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.


Definition and Examples of Vector Spaces, Subspaces, Algebra of subspaces, Linear span, Linear dependence and independence of vectors, Basis and Dimension of a vector space, Basis and dimension of subspace, Direct sums and complements.

Linear Transformations, Rank and Nullity of a linear transformation, Vector space of linear transformations.

Linear transformation and matrices, Change of basis.

Characteristic roots and characteristic vectors, Algebraic and Geometric multiplicity of a characteristic value, Cayley‑Hamilton theorem, Diagonalizable operators and matrices. Minimal polynomial of a linear operator (matrix).

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