Linear Algebra I Matrices and Row operations
Publisher: Bookboon
Published: 2013
ISBN-13: 9788740300109
Table of contents: title: Preface; title: Preliminaries; title: Sets And Set Notation; title: Functions; title: The Number Line And Algebra Of The Real Numbers; title: Ordered fields; title: The Complex Numbers; title: Exercises; title: Completeness of R; title: Well Ordering And Archimedean Property; title: Division And Numbers; title: Systems Of Equations; title: Exercises; title: Fn; title: Algebra in Fn; title: Exercises; title: The Inner Product In Fn; title: What Is Linear Algebra?; title: Exercises; title: Matrices And Linear Transformations; title: Matrices; title: Exercises; title: Linear Transformations; title: Subspaces And Spans; title: An Application To Matrices; title: Matrices And Calculus; title: Exercises; title: Determinants; title: Basic Techniques And Properties; title: Exercises; title: The Mathematical Theory Of Determinants; title: The Cayley Hamilton Theorem; title: Block Multiplication Of Matrices; title: Exercises; title: Row Operations; title: Elementary Matrices; title: The Rank Of A Matrix; title: The Row Reduced Echelon Form; title: Rank And Existence Of Solutions To Linear Systems; title: Fredholm Alternative; title: Exercises; title: Some Factorizations; title: LU Factorization; title: Finding An LU Factorization; title: Solving Linear Systems Using An LU Factorization; title: The PLU Factorization; title: Justification For The Multiplier Method; title: Existence For The PLU Factorization; title: The QR Factorization; title: Exercises; title: Linear Programming; title: Simple Geometric Considerations; title: The Simplex Tableau; title: The Simplex Algorithm; title: Finding A Basic Feasible Solution; title: Duality; title: Exercises