Advanced Linear Algebra with Applications 1st ed. 2022

This is a comprehensive textbook of linear algebra, intended for advanced undergraduate students of mathematics. Throughout the text, proofs have been made direct and simple without irrelevant details. It needs no prerequisites except some basic knowledge of sets, mappings and number systems. The topics have been presented in a simple and coherent style. The book starts with a quick review of basic literature on groups, rings and fields and ends with the applications of linear algebra in analytical geometry and numerical methods. It also includes a number of exercises and examples at the end of each chapter to enhance the understanding of readers. The subject is developed in a manner accessible to students with little knowledge of linear algebra. Chapters 1–6 discuss introductory topics like groups, rings, fields, matrices, determinants, systems of linear equations, vector spaces, linear transformations, dual spaces, and inner product spaces, which are taught at the first course of linear algebra at the undergraduate level. Chapters 7–9 cover advanced topics like canonical, bilinear, quadratic, sesquilinear and Hermitian forms of operators and matrices, which are taught at the advanced undergraduate course in mathematics. Chapters 10–12 focus on empowering readers to pursue interdisciplinary applications of linear algebra and illustrate the power of the subject through a variety of applications in numerical methods, analytical geometry and in solving linear system of differential equations.