Linear Algebra For Dummies book cover

Linear Algebra For Dummies

Author:
Mary Jane Sterling
Published: July 7, 2009

Overview

Learn to:

  • Solve linear algebra equations in several ways
  • Put data in order with matrices
  • Determine values with determinants
  • Work with eigenvalues and eigenvectors

Your hands-on guide to real-world applications of linear algebra

Does linear algebra leave you feeling lost? No worries —this easy-to-follow guide explains the how and the why of solving linear algebra problems in plain English. From matrices to vector spaces to linear transformations, you'll understand the key concepts and see how they relate to everything from genetics to nutrition to spotted owl extinction.

  • Line up the basics — discover several different approaches to organizing numbers and equations, and solve systems of equations algebraically or with matrices
  • Relate vectors and linear transformations — link vectors and matrices with linear combinations and seek solutions of homogeneous systems
  • Evaluate determinants — see how to perform the determinant function on different sizes of matrices and take advantage of Cramer's rule
  • Hone your skills with vector spaces — determine the properties of vector spaces and their subspaces and see linear transformation in action
  • Tackle eigenvalues and eigenvectors — define and solve for eigenvalues and eigenvectors and understand how they interact with specific matrices

Open the book and find:

  • Theoretical and practical ways of solving linear algebra problems
  • Definitions of terms throughout and in the glossary
  • New ways of looking at operations
  • How linear algebra ties together vectors, matrices, determinants, and linear transformations
  • Ten common mathematical representations of Greek letters
  • Real-world applications of matrices and determinants

Learn to:

  • Solve linear algebra equations in several ways
  • Put data in order with matrices
  • Determine values with determinants
  • Work with eigenvalues and eigenvectors

Your hands-on guide to real-world applications of linear algebra

Does linear algebra leave you feeling lost? No worries —this easy-to-follow guide explains the how and the why of solving linear algebra problems in plain English. From matrices to vector spaces to linear transformations, you'll understand the key concepts and see how they relate to everything from genetics to nutrition to spotted owl extinction.

  • Line up the basics — discover several different approaches to organizing numbers and equations, and solve systems of equations algebraically or with matrices
  • Relate vectors and linear transformations — link vectors and matrices with linear combinations and seek solutions
of homogeneous systems
  • Evaluate determinants — see how to perform the determinant function on different sizes of matrices and take advantage of Cramer's rule
  • Hone your skills with vector spaces — determine the properties of vector spaces and their subspaces and see linear transformation in action
  • Tackle eigenvalues and eigenvectors — define and solve for eigenvalues and eigenvectors and understand how they interact with specific matrices
  • Open the book and find:

    • Theoretical and practical ways of solving linear algebra problems
    • Definitions of terms throughout and in the glossary
    • New ways of looking at operations
    • How linear algebra ties together vectors, matrices, determinants, and linear transformations
    • Ten common mathematical representations of Greek letters
    • Real-world applications of matrices and determinants
    Linear Algebra For Dummies Cheat Sheet

    To study and solve linear algebra equations successfully, you need to know common numerical values of trig functions, what elements determine a vector space, basic algebraic properties, and general commands using graphing calculators to solve linear algebra problems.

    Articles From The Book

    4 results

    Algebra Articles

    Algebraic Properties You Should Know

    You can use a number of properties when working with linear algebraic expressions, including the commutative, associative, and distributive properties of addition and multiplication, as well as identities and inverses in addition and multiplication:

    Algebra Articles

    Commonly Used Values of Selected Trig Functions

    When performing transformations in trig functions, such as rotations, you need to use the numerical values of these functions. Here are some of the more commonly used angles.

    Algebra Articles

    How to Meet Vector Space Requirements

    In linear algebra, a set of elements is termed a vector space when particular requirements are met. For example, let a set consist of vectors u, v, and w. Also let k and l be real numbers, and consider the defined operations of ⊕ and ⊗. The set is a vector space if, under the operation of ⊕, it meets the following requirements:

    • Closure. uv is in the set.

    • Commutativity. uv = vu.

    • Associativity. u ⊕ (vw) = (uv) ⊕ w.

    • An identity element 0. u0 = 0u = u for any element u.

    • An inverse element −u. u−u = −u u = 0

    Under the operation of ⊗, the set is a vector space if it meets the following requirements:

    • Closure. ku is in the set.

    • Distribution over a vector sum. k ⊗ (uv) = kukv.

    • Distribution over a scalar sum. (k + l) ⊗ u = kulu.

    • Associativity of a scalar product. k ⊗ (lu) = (kl) ⊗ u.

    • Multiplication by the scalar identity. 1 ⊗ u = u.