Summary We investigate estimation of a normal mean matrix under the quadratic loss. Improved loss implies improved any linear combination columns First, an unbiased estimate risk is derived and Efron–Morris estimator shown to be minimax. Next, notion superharmonicity for matrix-variate functions introduced have properties analogous those usual superharmonic functions, which may independent inte...

We show that any regular quadratic matrix polynomial can be reduced to an upper triangular quadratic matrix polynomial over the complex numbers preserving the finite and infinite elementary divisors. We characterize the real quadratic matrix polynomials that are triangularizable over the real numbers and show that those that are not triangularizable are quasi-triangularizable with diagonal bloc...

in this paper, an optimal control of quadratic performance index with nonlinear constrained is presented. the sine-cosine wavelet operational matrix of integration and product matrix are introduced and applied to reduce nonlinear differential equations to the nonlinear algebraic equations. then, the newton-raphson method is used for solving these sets of algebraic equations. to present ability ...

We introduce and study a special class of nonconvex quadratic problems in which the objective and constraint functions have the form f(X) = Tr(XAX)+2Tr(BX)+c,X ∈ RRn×r. The latter formulation is termed quadratic matrix programming (QMP) of order r. We construct a specially devised semidefinite relaxation (SDR) and dual for the QMP problem and show that under some mild conditions strong duality ...

In Nonnegative Matrix Factorization (NMF), a nonnegative matrix is approximated by a product of lower-rank factorizing matrices. Most NMF methods assume that each factorizing matrix appears only once in the approximation, thus the approximation is linear in the factorizing matrices. We present a new class of approximative NMF methods, called Quadratic Nonnegative Matrix Factorization (QNMF), wh...

In this article, we characterize the involutiveness of the linear combination of the forma1A1 +a2A2 when a1, a2 are nonzero complex numbers, A1 is a quadratic or tripotent matrix,and A2 is arbitrary, under certain properties imposed on A1 and A2.