## Topics in Matrix AnalysisBuilding on the foundations of its predecessor volume, Matrix Analysis, this book treats in detail several topics with important applications and of special mathematical interest in matrix theory not included in the previous text. These topics include the field of values, stable matrices and inertia, singular values, matrix equations and Kronecker products, Hadamard products, and matrices and functions. The authors assume a background in elementary linear algebra and knowledge of rudimentary analytical concepts. The book should be welcomed by graduate students and researchers in a variety of mathematical fields both as an advanced text and as a modern reference work. |

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### Contents

II | 1 |

III | 5 |

IV | 8 |

V | 17 |

VI | 28 |

VII | 30 |

VIII | 48 |

IX | 65 |

XXVII | 241 |

XXVIII | 242 |

XXIX | 254 |

XXX | 268 |

XXXI | 288 |

XXXII | 298 |

XXXIII | 304 |

XXXIV | 308 |

### Common terms and phrases

analytic assertion coefficients column commutes complex conclude consider continuously differentiable convex matrix function Corollary decreasingly ordered defined denote diagonalizable diagonally dominant doubly stochastic e Mn eigenvalues eigenvector equivalent example Exercise field of values formula function f(t function on Hn(a,b given matrix Hadamard product half-plane Hermitian matrices identity inequalities Jordan blocks Jordan canonical form Kronecker product Lemma Linear Algebra Appl M-matrix main diagonal entries Math matrix equations matrix norm minimal polynomial Mn be given Mn(R monotone matrix function multiplicities nonnegative nonnegative matrix nonsingular nonzero norm on Mn normal normal matrix nullspace orthogonal permutation matrix positive definite matrices positive semidefinite positive stable primary matrix function principal submatrix Problem rank result satisfies scalar Schur Section singular value decomposition solution spectral norm square root suppose symmetric tion unitarily invariant norm unitarily similar unitary matrix upper triangular Verify weak majorization zero