Mathematical Sciences: RUI: Matrix Equations, Inertia and Stability

这项研究将涉及几个核心问题， 线性代数领域：矩阵方程、惯性和 稳定性，这与计算线性 代数和控制理论。 第一，研究条件 西尔维斯特、李雅普诺夫和里卡蒂解的非奇异性 将学习矩阵方程。 第二，校长 研究人员计划研究矩阵的正交解 方程 第三，首席研究员计划研究 具有特殊性质的对称化子的构造 应用. 第四，主要研究者将研究 惯性理论的几个领域，即奇异惯性理论， Riccati方程的惯性理论和广义惯性。 最后，主要研究者将在阳性时进行研究 正定矩阵有正定象和半正定象 在某些李雅普诺夫映射下

This research will concern itself with several of the core areas of linear algebra: matrix equations, inertia, and stability, which have relevance both to computational linear algebra and to control theory. First the study of conditions for nonsingularity of solutions of Sylvester, Lyapunov, and Riccati matrix equations will be studied. Second the principal investigator plans to study orthogonal solutions of matrix equations. Third the principal investigator plans to study the construction of symmetrizers with specific properties of use in applications. Fourth the principal investigator will study several areas of inertia theory, namely singular inertia theory, inertia theory for Riccati equations, and generalized inertia. Finally the principal investigator will study when positive definite matrices have positive definite and semidefinite images under certain Lyapunov maps.