## Indefinite Linear Algebra and ApplicationsThis book covers recent results in linear algebra with indefinite inner product. It includes applications to differential and difference equations with symmetries, matrix polynomials and Riccati equations. These applications are based on linear algebra in spaces with indefinite inner product. The latter forms an independent branch of linear algebra called indefinite linear algebra. This new subject is presented following the principles of a standard linear algebra course. |

### Contents

1 | |

7 | |

Orthogonalization and Orthogonal Polynomials | 19 |

Classes of Linear Transformations | 45 |

Canonical Forms | 73 |

Real HSelfadjoint Matrices | 125 |

Functions of HSelfadjoint Matrices | 143 |

HNormal Matrices | 159 |

Definite Invariant Subspaces | 207 |

Differential Equations of First Order | 229 |

Matrix Polynomials | 237 |

Differential and Difference Equations of Higher Order | 267 |

Algebraic Riccati Equations | 289 |

A Topics from Linear Algebra | 319 |

348 | |

355 | |

### Other editions - View all

Indefinite Linear Algebra and Applications Israel Gohberg,Peter Lancaster,Leiba Rodman No preview available - 2009 |

Indefinite Linear Algebra and Applications Israel Gohberg,Peter Lancaster,Leiba Rodman No preview available - 2005 |

### Common terms and phrases

A-invariant analytic applies Assume basis called canonical form Chapter closed Cn×n coefficients complex connected components consider continuous controllable corresponding defined determined diag diagonal differential direct easily eigenvectors equal equation equivalent example Exercise exists fact Find fixed follows formula function given H-selfadjoint H-selfadjoint matrix H-unitary hence hermitian matrix hermitian solution holds implies indefinite inner product invariant invertible Jordan blocks Jordan form leading Lemma linear transformation matrix polynomial maximal multiplicities negative neighborhood nonreal nonzero Note observe obtain orthogonal pair partial multiplicities particular perturbation positive definite proof proof of Theorem Proposition prove Range real eigenvalues resp respect result root subspaces satisfying seen shows sign characteristic similar simple sizes space Span standard statement structure subspace sufficiently Theorem theory unique unit circle unitary vectors zero

### References to this book

Exponentially Dichotomous Operators and Applications Cornelis V. M. van der Mee Limited preview - 2008 |