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MATLAB Matrix Algebra

Book Description

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MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java.

MATLAB Matrix Algebra introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. Starting with a look at symbolic and numeric variables, with an emphasis on vector and matrix variables, you will go on to examine functions and operations that support vectors and matrices as arguments, including those based on analytic parent functions. Computational methods for finding eigenvalues and eigenvectors of matrices are detailed, leading to various matrix decompositions. Applications such as change of bases, the classification of quadratic forms and how to solve systems of linear equations are described, with numerous examples. A section is dedicated to sparse matrices and other types of special matrices. In addition to its treatment of matrices, you will also learn how MATLAB can be used to work with arrays, lists, tables, sequences and sets.

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Table of Contents

  1. Cover
  2. Title
  3. Copyright
  4. Contents at a Glance
  5. Contents
  6. About the Author
  7. Chapter 1: Matrix and Vector Variables (Numeric and Symbolic)
    1. 1.1 Variables
    2. 1.2 Variables and Special Constants
    3. 1.3 Symbolic and Numeric Variables
    4. 1.4 Vector Variables
    5. 1.5 Matrix Variables
    6. 1.6 Character Variables
    7. 1.7 Operators
      1. 1.7.1 Arithmetic Operators
      2. 1.7.2 Relational Operators
      3. 1.7.3 Logical Operators
    8. 1.8 Logic Functions
    9. 1.9 Elementary Functions that Support Complex Matrix Arguments
    10. 1.10 Elementary Functions that Support Complex Vector Arguments
    11. 1.11 Vector Functions of Several Variables
      1. 1.11.1 Functions of One Variable
  8. Chapter 2: Matrix Algebra
    1. 2.1 Vectors and Matrices
    2. 2.2 Operations with Numeric Matrices
    3. 2.3 Eigenvalues and Eigenvectors
      1. 2.3.1 Numeric Matrices
      2. 2.3.2 Symbolic Matrices
    4. 2.4 Matrix Decomposition
    5. 2.5 Equivalent Matrices and Diagonalization
    6. 2.6 Sparse Matrices
      1. 2.6.1 Special Matrices
  9. Chapter 3: Sequences, Arrays, Tables, Lists and Sets
    1. 3.1 Sequences
    2. 3.2 Arrays
    3. 3.3 Relationships Between Vectors, Matrices and Arrays
      1. 3.3.1 Tables
    4. 3.5 Lists
      1. 3.5.1 Selecting and Manipulating Elements From Lists
      2. 3.5.2 Ordering and Applying Functions to Lists
      3. 3.5.3 Performing Operations With Elements of Lists
      4. 3.5.4 Sets
  10. Chapter 4: Vector Spaces and Linear Applications. Equations and Systems
    1. 4.1 Matrix Algebra and Vector Spaces
    2. 4.2 Linear Independence, Bases, and Base Change
    3. 4.3 Vector Geometry in 2 and 3 Dimensions
    4. 4.4 Linear Applications
    5. 4.5 Quadratic Forms
    6. 4.6 Equations and Systems
    7. 4.7 Systems of Linear Equations
    8. 4.8 The Rouche-Frobenius Theorem
    9. 4.9 Homogeneous Systems
  11. Chapter 5: Vector and Matrix Functions of Complex Variables
    1. 5.1 Complex Numbers
    2. 5.2 General Functions of a Complex Variable
      1. 5.2.1 Trigonometric Functions of a Complex Variable
      2. 5.2.2 Hyperbolic Functions of a Complex Variable
      3. 5.2.3 Exponential and Logarithmic Functions of a Complex Variable
      4. 5.2.4 Specific Functions of a Complex Variable
    3. 5.3 Basic Functions with Complex Vector Arguments
    4. 5.4 Basic Functions with Complex Matrix Arguments
    5. 5.5 General Functions with Complex Matrix Arguments
      1. 5.5.1 Trigonometric Functions of a Complex Matrix Variable
      2. 5.5.2 Hyperbolic Functions of a Complex Matrix Variable
      3. 5.5.3 Exponential and Logarithmic Functions of Complex Matrix Variables
      4. 5.5.4 Specific Features of Complex Matrices
    6. 5.6 Operations with Real and Complex Variables