## A Course in Linear Algebra with ApplicationsThis is the second edition of the best-selling introduction to linear algebra. Presupposing no knowledge beyond calculus, it provides a thorough treatment of all the basic concepts, such as vector space, linear transformation and inner product. The concept of a quotient space is introduced and related to solutions of linear system of equations, and a simplified treatment of Jordan normal form is given.Numerous applications of linear algebra are described, including systems of linear recurrence relations, systems of linear differential equations, Markov processes, and the Method of Least Squares. An entirely new chapter on linear programing introduces the reader to the simplex algorithm with emphasis on understanding the theory behind it.The book is addressed to students who wish to learn linear algebra, as well as to professionals who need to use the methods of the subject in their own fields. |

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### Contents

Chapter One Matrix Algebra | 1 |

Chapter Two Systems of Linear Equations | 30 |

Chapter Three Determinants | 57 |

Chapter Four Introduction to Vector Spaces | 87 |

Chapter Five Basis and Dimension | 112 |

Chapter Six Linear Transformations | 152 |

Chapter Seven Orthogonality in Vector Spaces | 193 |

Chapter Eight Eigenvectors and Eigenvalues | 257 |

Chapter Nine More Advanced Topics | 303 |

Chapter Ten Linear Programming | 370 |

Appendix Mathematical Induction | 415 |

430 | |

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### Common terms and phrases

arbitrary basic feasible solution bilinear form canonical form characteristic polynomial coefficient matrix column space column vector compute convex corresponding coset defined denote det(A determinant diagonalizable dimension eigenvalues eigenvectors elements equals Example Exercises extreme points form a basis function Hence inner product space integers invertible matrix isomorphic Jordan normal form least squares solution line segments linear combination linear operator linear programming linear programming problem linear system linear system AX linear transformation linearly independent m x n maximize minimum polynomial n x n matrix null space number of pivots obtain optimal solution ordered basis orthonormal basis permutation Proof Prove quadratic form real numbers reduced row echelon represented respectively row echelon form row space scalar multiplication skew-symmetric solve square matrix subset subspace Suppose systems of linear tableau Theorem tion unique upper triangular variables vector space XTAX zero vector