A First Course in Linear Algebra

A First Course in Linear Algebra

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This text, originally by K. Kuttler, has been redesigned by the Lyryx editorial team as a first course in linear algebra for science and engineering students who have an understanding of basic algebra. All major topics of linear algebra are available in detail, as well as proofs of important theorem...

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Bibliographic Details
Main Author: Kuttler, Ken (Author)
Format: Electronic eBook
Language:English
Published: [Place of publication not identified] Lyryx 2017.
Series:Open textbook library.
Subjects:
Mathematics > Textbooks
Algebra > Textbooks
Online Access:Access online version
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Table of Contents:
  • 1 Systems of Equations
  • 1.1 Systems of Equations, Geometry
  • 1.2 Systems Of Equations, Algebraic Procedures
  • 2 Matrices
  • 2.1 Matrix Arithmetic
  • 2.2 LU Factorization
  • 3 Determinants
  • 3.1 Basic Techniques and Properties
  • 3.2 Applications of the Determinant
  • 4 R^n
  • 4.1 Vectors in R^n
  • 4.2 Algebra in R^n
  • 4.3 Geometric Meaning of Vector Addition
  • 4.4 Length of a Vector
  • 4.5 Geometric Meaning of Scalar Multiplication
  • 4.6 Parametric Lines
  • 4.7 The Dot Product
  • 4.8 Planes in R^n
  • 4.9 The Cross Product
  • 4.10 Spanning, Linear Independence and Basis in R^n
  • 4.11 Orthogonality and the Gram Schmidt Process
  • 4.12 Applications
  • 5 Linear Transformations
  • 5.1 Linear Transformations
  • 5.2 The Matrix of a Linear Transformation I
  • 5.3 Properties of Linear Transformations
  • 5.4 Special Linear Transformations in R^2
  • 5.5 One to One and Onto Transformations
  • 5.6 Isomorphisms
  • 5.7 The Kernel And Image Of A Linear Map
  • 5.8 The Matrix of a Linear Transformation II
  • 5.9 The General Solution of a Linear System
  • 6 Complex Numbers
  • 6.1 Complex Numbers
  • 6.2 Polar Form
  • 6.3 Roots of Complex Numbers
  • 6.4 The Quadratic Formula
  • 7 Spectral Theory
  • 7.1 Eigenvalues and Eigenvectors of a Matrix
  • 7.2 Diagonalization
  • 7.3 Applications of Spectral Theory
  • 7.4 Orthogonality
  • 8 Some Curvilinear Coordinate Systems
  • 8.1 Polar Coordinates and Polar Graphs
  • 8.2 Spherical and Cylindrical Coordinates
  • 9 Vector Spaces
  • 9.1 Algebraic Considerations
  • 9.2 Spanning Sets
  • 9.3 Linear Independence
  • 9.4 Subspaces and Basis
  • 9.5 Sums and Intersections
  • 9.6 Linear Transformations
  • 9.7 Isomorphisms
  • 9.8 The Kernel And Image Of A Linear Map
  • 9.9 The Matrix of a Linear Transformation
  • A Some Prerequisite Topics
  • A.1 Sets and Set Notation
  • A.2 Well Ordering and Induction
  • B Selected Exercise Answers

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