## Linear Algebra and Its ApplicationsPraise for the First Edition ". . .recommended for the teacher and researcher as well as for graduate students. In fact, [it] has a place on every mathematician's bookshelf." -American Mathematical Monthly Linear Algebra and Its Applications, Second Edition presents linear algebra as the theory and practice of linear spaces and linear maps with a unique focus on the analytical aspects as well as the numerous applications of the subject. In addition to thorough coverage of linear equations, matrices, vector spaces, game theory, and numerical analysis, the Second Edition features student-friendly additions that enhance the book's accessibility, including expanded topical coverage in the early chapters, additional exercises, and solutions to selected problems. Beginning chapters are devoted to the abstract structure of finite dimensional vector spaces, and subsequent chapters address convexity and the duality theorem as well as describe the basics of normed linear spaces and linear maps between normed spaces. Further updates and revisions have been included to reflect the most up-to-date coverage of the topic, including: - The QR algorithm for finding the eigenvalues of a self-adjoint matrix
- The Householder algorithm for turning self-adjoint matrices into tridiagonal form
- The compactness of the unit ball as a criterion of finite dimensionality of a normed linear space
Clear, concise, and superbly organized, Linear Algebra and Its Applications, Second Edition serves as an excellent text for advanced undergraduate- and graduate-level courses in linear algebra. Its comprehensive treatment of the subject also makes it an ideal reference or self-study for industry professionals. |

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Excellent. Not at all introductory. I use it for important topics not in the official curriculum.

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Presents advanced material in a way that avoids overly messy generalizations. A great reference book if you need to get work done. Also the proofs are very nicely explained. Highly recommended.

### Contents

Fundamentals | 1 |

Duality | 13 |

Linear Mappings | 19 |

Matrices | 32 |

Determinant and Trace | 44 |

Spectral Theory | 58 |

Euclidean Structure | 77 |

Spectral Theory of SelfAdjoint Mappings | 101 |

Positive Matrices | 237 |

How to Solve Systems of Linear Equations | 246 |

How to Calculate the Eigenvalues of SelfAdjoint Matrices | 262 |

Solutions | 278 |

Bibliography | 300 |

Symplectic Matrices | 308 |

Lattices | 317 |

Gershgorins Theorem | 323 |

Calculus of Vector and MatrixValued Functions | 121 |

Matrix Inequalities | 143 |

Kinematics and Dynamics | 172 |

Convexity | 187 |

The Duality Theorem | 202 |

Normed Linear Spaces | 214 |

Linear Mappings Between Normed Linear Spaces | 229 |

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### Common terms and phrases

2007 John Wiley Â n matrix According to Theorem adjoint algorithm anti-self-adjoint Applications belongs called Chapter characteristic polynomial choose claim Clearly coefﬁcients commute completes the proof complex numbers components converges convex set Corollary deduce deﬁned Deﬁnition denote determinant diagonal entries dimension dimensional dimX eigenvalues eigenvectors equal equation Euclidean space Euclidean structure Exercise ﬁnite ﬁnite-dimensional ﬁrst follows formula inequality integral invertible isometry isomorphism Lax Copyright Lemma Linear Algebra linear combination linear function linear map linearly independent Lorentz transformation multiplication nonnegative nonzero normed linear space nullspace orthogonal polynomial of degree proof of Theorem properties real numbers rewrite right-hand side root rotation satisﬁes satisfy scalar product Second Edition self-adjoint mapping self-adjoint matrices sequence Show solution spectral spectral theory subspace Suppose symmetric symplectic matrices tends to zero Theorem 12 transpose unit vectors Wiley & Sons