## Applications of the Theory of MatricesThis text features material of interest to applied mathematicians as well as to control engineers studying stability of a servo-mechanism and numerical analysts evaluating the roots of a polynomial. Includes complex symmetric, antisymmetric, and orthogonal matrices; singular bundles of matrices and matrices with nonnegative elements. Also features linear differential equations and the Routh-Hurwitz problem. 1959 edition. |

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adjoint matrix antisymmetric matrix arbitrary canonical form Cauchy index column constant matrix converges COROLLARY 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 formula Hankel matrix Hence Hermitian holds homogeneous Markov chain Hurwitz determinants Hurwitz polynomial inequalities infinite Hankel matrix irreducible matrix lemma linear linearly independent Lyapunov transformation Markov chain Markov parameters minimal indices multiplied necessary and sufficient negative real nonnegative matrix nonsingular nonzero normal form number of roots obtain orthogonal matrix pencil of matrices permutation positive pair principal minors proof properties quadratic forms rational function real numbers real polynomial f(z real roots reducible relation replaced right half-plane right member Routh scheme Routh-Hurwitz Routh-Hurwitz theorem rows satisfy Section singular point stochastic matrix strictly equivalent subspace sufficient condition symmetric matrix