A class of marked invariant subspaces with an application to algebraic Riccati equations

TL;DR

The paper characterizes a special class of invariant subspaces of matrices that are basis-independent and applies this theory to Hamilton matrices and algebraic Riccati equations.

Contribution

It introduces a new class of invariant subspaces invariant under basis choice and applies this to problems involving Hamilton matrices and Riccati equations.

Findings

Identifies basis-independent invariant subspaces derived from Jordan bases.

Provides a characterization of these subspaces.

Applies the results to algebraic Riccati equations.

Abstract

Invariant subspaces of a matrix $A$ are considered which are obtained by truncation of a Jordan basis of a generalized eigenspace of $A$. We characterize those subspaces which are independent of the choice of the Jordan basis. An application to Hamilton matrices and algebraic Riccati equations is given.