Matrix analysis
Applied numerical linear algebra
Applied numerical linear algebra
Fast reliable algorithms for matrices with structure
Fast reliable algorithms for matrices with structure
Isospectral flows on displacement structured matrix spaces
Structured matrices
Nonlinear Control Systems: An Introduction
Nonlinear Control Systems: An Introduction
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I show that manifolds arise naturally when we consider structured eigen-problems for symmetric matrices. In particular, I show that the space of symmetric matrices is naturally partitioned into a collection S of connected submanifolds with the following property: For every symmetric matrix A, the submanifold in S containing A consists of matrices which have the same eigenvalues as A and the same staircase structure as A. I also show that the space of symmetric matrices is naturally partitioned into a collection T of connected submanifolds with the following property: For every symmetric matrix A, the submanifold in T containing A consists of matrices which have the same eigenvalues as A and the same displacement inertia as A. I obtain these results by considering appropriate Lie algebras of vector fields on the space of symmetric matrices.