Nonnegative Definite Solutions Research Articles

Hermitian and Nonnegative Definite Solutions of Linear Matrix Equations

Necessary and sufficient conditions for existence and expressions for general Hermitian and nonnegative definite solutions are obtained for the following three systems of linear equations: (I) $AX = C$, (II) $AX = C,XB = D$, (III) $AXB = C$.

On Nonnegative Definite Solutions to Matrix Quadratic Equations

Summary The problem of finding all nonnegative definite solutions to the “Riccati” algebraic equation PA + A'P - PBB'P + C'C = 0 is solved in general. The class of such solutions is shown to constitute a distributive lattice. Finally an algorithm to compute those solutions without checking all general solutions is proposed.

Non-negative definite solutions of certain differential and functional equations

Non-negative definite solutions of certain differential and functional equations

Conditions for Positive and Nonnegative Definiteness in Terms of Pseudoinverses

Matrix pseudoinverses producing necessary and sufficient conditions for positive and nonnegative definiteness

Matrix Quadratic Solutions

Matrix quadratic equation solution derivation applied in finding steady state solutions of Riccati differential equations with constant coefficients