This is a guide to linear algebra, designed for beginners with little or no prior knowledge of the subject. kunze hoffman linear algebra pdf This first chapter is a quick review of elementary matrices and determinants. The second chapter covers the fundamentals of linear equations (Chapter 1) and systems of linear equations (Chapter 2). Chapter 3 examines the basic properties of determinants and the volume of the eigenvalue-eigenvector pairs of a matrix, which leads us to the famous inverse theorem in linear algebra. Chapter 4 covers diagonalization which gives us a new way to solve systems of equations by reducing them to simpler, equivalent problems in terms of vectors only. Chapter 5 discusses various methods for solving systems including Gaussian elimination, Lyndon–Morrison–Woodbury formula, methods based on geometrical transformations and finally, an approximate method based on graph minorants.

Hoffman, Kunze – Linear Algebra provides a thorough introduction to linear algebra. The book starts by laying the foundations of linear algebra from a historical and pedagogical point of view and is designed for use in courses on linear algebra, advanced calculus, and continuous mathematics. This is followed by an introduction to matrix theory, which is the central topic of linear algebra, as it explains all other concepts using matrix methods. This second edition includes updated information on recent advances in the field.

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