This book is intended for an introductory course in linear algebra for undergraduate students of mathematics. It deals with the concept of vector spaces and special types of functions defined on them called linear transformations or operators. The vector spaces considered in the book are finite-dimensional, a concept that involves the representation of vectors in terms of a finite number of vectors which form a basis for the vector spaces. The book also offers an introduction to Hilbert Space Theory. The generic model of a finite-dimensional Hilbert space (real or complex) is IRn or sn but the true relevance of operators in Hilbert spaces surfaces only when they are infinite-dimensional. In order to properly comprehend the structure of an infinite-dimensional Hilbert space, it is important to grasp it at the finite-dimensional level. Finite-dimensional Hilbert spaces are discussed comprehensively in the first eight chapters; in the last three chapters the treatment of Hilbert spaces is given in a setting which can be easily extended to defining infinite-dimensional Hilbert spaces. After using this textbook, students will have a clear understanding of the model of a Hilbert space in finite-dimensions and will be able to smoothly make the transition to infinite-dimensional Hilbert Space Theory. Written from a student’s perspective, this textbook includes numerous solved examples and exercises at the end of each section to help students gain confidence in his/her analytical skills.

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