Scientific Research Publishing

Derivative of a Determinant with Respect to an Eigenvalue in the Modified Cholesky Decomposition of a Symmetric Matrix, with Applications to Nonlinear Analysis ()

In this paper, we obtain a formula for the derivative of a determinant with respect to an eigenvalue in the modified Cholesky decomposition of a symmetric matrix, a characteristic example of a direct ...
Scientific Research Publishing

Derivative of a Determinant with Respect to an Eigenvalue in the LDU Decomposition of a Non-Symmetric Matrix ()

In previous work, the author used the trace theorem and the inverse matrix formula for the coefficient matrix appearing in the conjugate gradient method to propose a method for derivative a ...
JSTOR Daily

On the Existence of Moments of Ratios of Quadratic Forms

We obtain simple and generally applicable conditions for the existence of mixed moments E([X′ AX]u/[X′ BX]v) of the ratio of quadratic forms T = X′AX/X′BX, where A and B are n × n symmetric matrices ...
JSTOR Daily

Proof of Conjectures About the Expected Values of the Elementary Symmetric Functions of a Noncentral Wishart Matrix

This paper provides proof of conjectures about the expected values of the jth elementary symmetric function of the roots (i.e. $E(\operatorname{tr}_j A)$) of a non ...
IEEE

Bonhihotri Hazra

Algebraic Riccati Equation,Control Input,Control Strategy,Cost Function,Definite Matrix,Differential Equations,Feedback Control,Feedback Gain Matrix,Gain Control,Gain ...