Elementary Linear Algebra
Publisher: Bookboon
Published: 2013
ISBN-13: 9788740300185
Table of contents: title: Some Prerequisite Topics; title: Sets And Set Notation; title: Functions; title: Graphs Of Functions; title: The Complex Numbers; title: Polar Form Of Complex Numbers; title: Roots Of Complex Numbers; title: The Quadratic Formula; title: Exercises; title: Fn; title: Algebra in Fn; title: Geometric Meaning Of Vectors; title: Geometric Meaning Of Vector Addition; title: Distance Between Points In Rn Length Of A Vector; title: Geometric Meaning Of Scalar Multiplication; title: Exercises; title: Vectors And Physics; title: Exercises; title: Vector Products; title: The Dot Product; title: The Geometric Significance Of The Dot Product; title: Exercises; title: The Cross Product; title: The Vector Identity Machine; title: Exercises; title: Systems Of Equations; title: Systems Of Equations, Geometry; title: Systems Of Equations, Algebraic Procedures; title: Exercises; title: Matrices; title: Matrix Arithmetic; title: Exercises; title: Determinants; title: Basic Techniques And Properties; title: Applications; title: Exercises; title: The Mathematical Theory Of Determinants; title: The Function sgnn; title: The Determinant; title: The Cayley Hamilton Theorem; title: Rank Of A Matrix; title: Elementary Matrices; title: THE Row Reduced Echelon Form Of A Matrix; title: The Rank Of A Matrix; title: Fredholm Alternative; title: Exercises; title: Linear Transformations; title: Linear Transformations; title: Constructing The Matrix Of A Linear Transformation; title: Exercises; title: The LU Factorization; title: Definition Of An LU factorization; title: Finding An LU Factorization By Inspection; title: Using Multipliers To Find An LU Factorization; title: Solving Systems Using The LU Factorization; title: Justification For The Multiplier Method; title: 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; title: Spectral Theory; title: Eigenvalues And Eigenvectors Of A Matrix; title: Some Applications Of Eigenvalues And Eigenvectors; title: The Estimation Of Eigenvalues; title: Exercises; title: Matrices And The Inner Product; title: Symmetric And Orthogonal Matrices; title: Fundamental Theory And Generalizations; title: Least Square Approximation; title: The Right Polar Factorization; title: The Singular Value Decomposition; title: Approximation In The Frobenius Norm; title: Moore Penrose Inverse; title: Exercises; title: Numerical Methods For Solving Linear Systems; title: Iterative Methods For Linear Systems; title: The Operator Norm; title: The Condition Number; title: Exercises; title: Numerical Methods For Solving The Eigenvalue Problem; title: The Power Method For Eigenvalues; title: The Shifted Inverse Power Method; title: The Rayleigh Quotient; title: The QR Algorithm; title: Exercises; title: Vector Spaces; title: Algebraic Considerations; title: Exercises; title: Vector Spaces And Fields; title: Exercises; title: Inner Product Spaces; title: Exercises; title: Linear Transformations; title: Matrix Multiplication As A Linear Transformation; title: L(V,W) As A Vector Space; title: Eigenvalues And Eigenvectors Of Linear Transformations; title: Block Diagonal Matrices; title: The Matrix Of A Linear Transformation; title: Exercises; title: The Jordan Canonical Form*; title: The Fundamental Theorem Of Algebra; title: Answers To Selected Exercises