This book is designed for use as a textbook for a formal course in linear algebra or as a supplement to all current standard texts. It aims to present an introduction to linear algebra which will be found helpful to all readers regardless of their fields of specification. More material has been included than can be covered in most first courses. This has been done to make the book more flexible, to provide a useful book of reference, and to stimulate further interest in the subject.

Linear algebra has in recent years become an essential part of the mathematical background required by mathematicians and mathematics teachers, engineers, computer scientists, physicists, economists, and statisticians, among others. This requirement reflects the importance and wide applications of the subject matter.

## Overview of Linear Algebra Schaum Series PDF

• Each chapter begins with clear statements of pertinent definitions, principles, and theorems together with illustrative and other descriptive material. This is followed by graded sets of solved and supplementary problems.
• The solved problems serve to illustrate and amplify the theory, and to provide the repetition of basic principles so vital to effective learning. Numerous proofs, especially those of all essential theorems, are included among the solved problems.
• The supplementary problems serve as a complete review of the material of each chapter.
• The first three chapters treat vectors in Euclidean space, matrix algebra, and systems of linear equations.
• These chapters provide the motivation and basic computational tools for the abstract investigations of vector spaces and linear mappings which follow.
• After chapters on inner product spaces and orthogonality and on determinants, there is a detailed discussion of eigenvalues and eigenvectors giving conditions for representing a linear operator by a diagonal matrix. This naturally leads to the study of various canonical forms, specifically, the triangular, Jordan, and rational canonical forms. Later chapters cover linear functions and the dual space V*, and bilinear, quadratic, and Hermitian forms.
• The last chapter treats linear operators on inner product spaces.

## Improvement in the Latest Edition of Linear Algebra Schaum Series PDF

The main changes in this edition have been in the appendices.

• First of all, we have expanded Appendix A on the tensor and exterior products of vector spaces where we have now included proofs of the existence and uniqueness of such products.
• Also added appendices covering algebraic structures, including modules, and polynomials over a field.
• Appendix D, ‘‘Odds and Ends,’’ includes the Moore–Penrose generalized inverse which appears in various applications, such as statistics.
• There are also many additional solved and supplementary problems.

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