Basic Linear Algebra is a textbook written by Cemal Koc, a professor of computer engineering at Naval Postgraduate School in Monterey, California. The book covers the fundamental concepts and techniques of linear algebra, such as matrices, determinants, vector spaces, inner products, eigenvalues, eigenvectors, diagonalization, and applications. The book is intended for undergraduate students who have some background in calculus and discrete mathematics.
The book consists of six chapters and an appendix. The first chapter introduces matrices, their operations, properties, and special types. The second chapter deals with systems of linear equations and their solutions using row operations and matrix inverses. The third chapter defines determinants and their properties, and shows how they can be used to solve linear systems and find inverses. The fourth chapter introduces vector spaces, subspaces, linear dependence and independence, bases, dimension, coordinates, and some important subspaces associated with matrices. The fifth chapter defines inner products and norms on vector spaces, and discusses orthogonality, orthogonal and orthonormal bases, Gram-Schmidt process, orthogonal projections, least squares method, and Fourier series. The sixth chapter covers eigenvalues, eigenvectors, diagonalization of matrices, matrix exponentials, Cayley-Hamilton theorem, systems of linear differential equations, real symmetric matrices, and quadratic forms.
The book is well-written and organized, with clear explanations and examples. The book also contains many exercises at the end of each section, ranging from routine computations to more challenging problems. Some exercises require the use of a computer algebra system or a calculator. The book also provides hints and solutions to selected exercises at the end of the book. The appendix contains some useful facts and formulas from calculus and discrete mathematics.
Basic Linear Algebra by Cemal Koc is a comprehensive and accessible introduction to linear algebra for students who want to learn the subject in depth. The book can be used as a textbook for a one-semester or a two-quarter course in linear algebra, or as a reference for students who need to review the material for other courses or applications.
One of the strengths of the book is that it emphasizes the connections between linear algebra and other areas of mathematics and science, such as geometry, calculus, differential equations, cryptography, computer graphics, and signal processing. The book also illustrates how linear algebra can be used to model and solve real-world problems, such as encryption, image compression, curve fitting, and population dynamics. The book provides many examples and applications that show the relevance and usefulness of linear algebra in various fields.
Another strength of the book is that it adopts a balanced approach between theory and computation. The book explains the theoretical foundations and results of linear algebra, as well as the algorithms and methods for performing calculations and manipulations. The book also discusses the advantages and limitations of different techniques, and the trade-offs between speed and accuracy. The book encourages the use of technology to enhance learning and understanding, but also warns against relying too much on it without checking the validity and correctness of the results.
Basic Linear Algebra by Cemal Koc is a valuable resource for anyone who wants to learn or review linear algebra. The book covers the essential topics and concepts in a clear and rigorous manner, with plenty of examples and exercises to reinforce learning. The book also shows how linear algebra can be applied to various domains and problems, and how it relates to other branches of mathematics and science. The book is suitable for students, instructors, and practitioners who are interested in linear algebra and its applications. 061ffe29dd