Linear Algebra: A First Course with Applications

ISBN-13: 9781584887829 / Angielski / Twarda / 2008 / 752 str.

Larry E. Knop

Opis

As an alternative to traditional textbooks on the subject, Linear Algebra: A Bridge Approach provides detailed coverage of major linear algebraic topics along with an introduction to reading, writing, and understanding proofs. The author develops examples and then presents abstractions of them to show the importance of the material being studied. Vector spaces and associated structures are discussed early in the text to help with the transition from purely computational to more abstract concepts. Emphasizing the use of MATLABr, the book includes applications and real-world analogies to make the material accessible to students.

Spis treści

Preface for the Instructor Foreword A Little Logic Logical Foundations Logical Equivalences Sets and Set Notation Quantification An Introduction to Vector Spaces The Vector Space R2—The Basics The Vector Space R2—Beyond the Basics The Vector Spaces Rn—The Basics The Vector Spaces Rn—Beyond the Basics The Vector Spaces Rn—Lines and Planes Vector Spaces in General Vector Spaces: Setting the Rules Vector Spaces: On the Wild Side Subspaces Subspaces and Linear Equations Subspaces from Subsets A Numerical Interlude—Systems of Linear Equations Solving Linear Systems Systematic Solutions of Systems Technology and Linear Algebra The Structure of Vector Spaces Spanning Sets Linear Independence More on Linear Independence Linear Independence and Span Vector Space Bases The Dimension of a Vector Space Linear Transformations Transformation Fundamentals Vector Space Isomorphisms Linear Transformations and Matrices Matrix Representations of Transformations Matrices and Associated Vector Spaces Inverses in Matrix Multiplication Elementary Matrices Determinants An Introduction to Determinants Properties of Determinants Eigenvalues and Eigenvectors Eigenvalues, Eigenvectors, and Eigenspaces More on Eigenvalues, Eigenvectors, and Eigenspaces Forests, Digraphs, and PageRank Diagonalization Answers to Selected Problems Index

O autorze

Larry E. Knop