## Applications of the theory of matrices |

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### Contents

CONTENTS Chapter | 1 |

Some formulas for complex orthogonal and unitary matrices | 2 |

Polar decomposition of a complex matrix | 7 |

Copyright | |

49 other sections not shown

### Common terms and phrases

a0zn antisymmetric matrix arbitrary canonical form Cauchy index coefficients column complex constant matrix converges corresponding defined degree denote diagonal blocks different from zero differential equations domain G domain of stability dominant characteristic number elementary divisors elements equal to zero finite formula Hankel matrix Hence holds homogeneous Markov chain Hurwitz determinants Hurwitz polynomial inequalities infinite Hankel matrix irreducible matrix lemma linear linearly independent Lyapunov transformation Markov chain minimal indices multiplied necessary and sufficient negative real nonnegative matrix nonsingular normal form obtain orthogonal matrix pencil of matrices permutation positive pair principal minors proof quadratic forms rank rational function real numbers real polynomial f(z real roots reducible regular relation replaced right half-plane Routh scheme Routh-Hurwitz Routh-Hurwitz theorem rows satisfy Section singular point stochastic matrix strictly equivalent Sturm's theorem subspace sufficient condition symmetric matrix xv x2