## Basic Theorems in Matrix Theory |

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A. M. Ostrowski adjoint Ax=b Block decomposition Cayley-Hamilton characteristic polynomial characteristic roots Companion matrix complex numbers Computation Congruence Conjugate transpose Convergence Crout deﬁned denote diagonal matrix Direct sum disks Duke Math eigen Eigenvalues of Submatrices eigenvectors elementary divisors elementary polynomial Elementary properties elementary transformations entry exists Frobenius theorem Gram matrix Hilbert ill-conditioned Inequalities Connecting Rank Inequalities for eigenvalues Inequalities of Hadamard inequality 14 Inner product integers inverse Kantorovich inequality Kronecker product LDU decomposition Linear Equations linear transformations linearly independent main diagonal matrix theory method 16 Minimal Polynomial Minkowski monic n-vector National Bureau nonderogatory nonsingular norm normal matrix Notation Optimum Gradient Method Orthonormality permutation matrix Polar factorization positive definite positive semidefinite Power method Principal Idempotents Rational canonical form real numbers Research NBS row and column row column Schur's identity Seidel similarity invariants singular values Smith form solution subdeterminants Submatrix symmetric function Taussky triangular matrix unitary Wittmeyer process