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CITATION

McMahon, David. Linear Algebra Demystified. US: McGraw-Hill Professional, 2005.

Linear Algebra Demystified

Authors: David McMahon

Published:  October 2005

eISBN: 9780071490450 0071490450 | ISBN: 9780071465793
Read the ePub (4.58MB)
  • Contents
  • Preface
  • Chapter 1 Systems of Linear Equations
  • Consistent and Inconsistent Systems
  • Matrix Representation of a System of Equations
  • Solving a System Using Elementary Operations
  • Triangular Matrices
  • Elementary Matrices
  • Implementing Row Operations with Elementary Matrices
  • Homogeneous Systems
  • Gauss-Jordan Elimination
  • Quiz
  • Chapter 2 Matrix Algebra
  • Matrix Addition
  • Scalar Multiplication
  • Matrix Multiplication
  • Square Matrices
  • The Identity Matrix
  • The Transpose Operation
  • The Hermitian Conjugate
  • Trace
  • The Inverse Matrix
  • Quiz
  • Chapter 3 Determinants
  • The Determinant of a Third-Order Matrix
  • Theorems about Determinants
  • Cramer’s Rule
  • Properties of Determinants
  • Finding the Inverse of a Matrix
  • Quiz
  • Chapter 4 Vectors
  • Vectors in R[sup(n)]
  • Vector Addition
  • Scalar Multiplication
  • The Zero Vector
  • The Transpose of a Vector
  • The Dot or Inner Product
  • The Norm of a Vector
  • Unit Vectors
  • The Angle between Two Vectors
  • Two Theorems Involving Vectors
  • Distance between Two Vectors
  • Quiz
  • Chapter 5 Vector Spaces
  • Basis Vectors
  • Linear Independence
  • Basis Vectors
  • Completeness
  • Subspaces
  • Row Space of a Matrix
  • Null Space of a Matrix
  • Quiz
  • Chapter 6 Inner Product Spaces
  • The Vector Space R[sup(n)]
  • Inner Products on Function Spaces
  • Properties of the Norm
  • An Inner Product for Matrix Spaces
  • The Gram-Schmidt Procedure
  • Quiz
  • Chapter 7 Linear Transformations
  • Matrix Representations
  • Linear Transformations in the Same Vector Space
  • More Properties of Linear Transformations
  • Quiz
  • Chapter 8 The Eigenvalue Problem
  • The Characteristic Polynomial
  • The Cayley-Hamilton Theorem
  • Finding Eigenvectors
  • Normalization
  • The Eigenspace of an Operator A
  • Similar Matrices
  • Diagonal Representations of an Operator
  • The Trace and Determinant and Eigenvalues
  • Quiz
  • Chapter 9 Special Matrices
  • Symmetric and Skew-Symmetric Matrices
  • Hermitian Matrices
  • Orthogonal Matrices
  • Unitary Matrices
  • Quiz
  • Chapter 10 Matrix Decomposition
  • LU Decomposition
  • Solving a Linear System with an LU Factorization
  • SVD Decomposition
  • QR Decomposition
  • Quiz
  • Final Exam
  • Hints and Solutions
  • References
  • Index