Elementary Linear Algebra
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 Price: 129.00 kr
 Price: 129.00 kr
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About the book
Reviews
Brice Taylor ★★★★★
Excellent, very comprehensive, and well written. Includes problem sets and answers. Portions would be a great primer for a university class, and is a great reference for theory.
Description
This is an introduction to linear algebra. The main part of the book features row operations and everything is done in terms of the row reduced echelon form and specific algorithms. At the end, the more abstract notions of vector spaces and linear transformations on vector spaces are presented. This is intended to be a first course in linear algebra for students who are sophomores or juniors who have had a course in one variable calculus and a reasonable background in college algebra.
Content
 Some Prerequisite Topics
 Sets And Set Notation
 Functions
 Graphs Of Functions
 The Complex Numbers
 Polar Form Of Complex Numbers
 Roots Of Complex Numbers
 The Quadratic Formula
 Exercises
 Fn
 Algebra in Fn
 Geometric Meaning Of Vectors
 Geometric Meaning Of Vector Addition
 Distance Between Points In Rn Length Of A Vector
 Geometric Meaning Of Scalar Multiplication
 Exercises
 Vectors And Physics
 Exercises
 Vector Products
 The Dot Product
 The Geometric Significance Of The Dot Product
 Exercises
 The Cross Product
 The Vector Identity Machine
 Exercises
 Systems Of Equations
 Systems Of Equations, Geometry
 Systems Of Equations, Algebraic Procedures
 Exercises
 Matrices
 Matrix Arithmetic
 Exercises
 Determinants
 Basic Techniques And Properties
 Applications
 Exercises
 The Mathematical Theory Of Determinants
 The Function sgnn
 The Determinant
 The Cayley Hamilton Theorem
 Rank Of A Matrix
 Elementary Matrices
 THE Row Reduced Echelon Form Of A Matrix
 The Rank Of A Matrix
 Fredholm Alternative
 Exercises
 Linear Transformations
 Linear Transformations
 Constructing The Matrix Of A Linear Transformation
 Exercises
 The LU Factorization
 Definition Of An LU factorization
 Finding An LU Factorization By Inspection
 Using Multipliers To Find An LU Factorization
 Solving Systems Using The LU Factorization
 Justification For The Multiplier Method
 The PLU Factorization
 The QR Factorization
 Exercises
 Linear Programming
 Simple Geometric Considerations
 The Simplex Tableau
 The Simplex Algorithm
 Finding A Basic Feasible Solution
 Duality
 Exercises
 Spectral Theory
 Eigenvalues And Eigenvectors Of A Matrix
 Some Applications Of Eigenvalues And Eigenvectors
 The Estimation Of Eigenvalues
 Exercises
 Matrices And The Inner Product
 Symmetric And Orthogonal Matrices
 Fundamental Theory And Generalizations
 Least Square Approximation
 The Right Polar Factorization
 The Singular Value Decomposition
 Approximation In The Frobenius Norm
 Moore Penrose Inverse
 Exercises
 Numerical Methods For Solving Linear Systems
 Iterative Methods For Linear Systems
 The Operator Norm
 The Condition Number
 Exercises
 Numerical Methods For Solving The Eigenvalue Problem
 The Power Method For Eigenvalues
 The Shifted Inverse Power Method
 The Rayleigh Quotient
 The QR Algorithm
 Exercises
 Vector Spaces
 Algebraic Considerations
 Exercises
 Vector Spaces And Fields
 Exercises
 Inner Product Spaces
 Exercises
 Linear Transformations
 Matrix Multiplication As A Linear Transformation
 L(V,W) As A Vector Space
 Eigenvalues And Eigenvectors Of Linear Transformations
 Block Diagonal Matrices
 The Matrix Of A Linear Transformation
 Exercises
 The Jordan Canonical Form*
 The Fundamental Theorem Of Algebra
 Answers To Selected Exercises