Isospectral flows on symmetric matrices and the Riccati equation. (English) Zbl 0732.93045
Summary: Brockett has studied the ordinary differential equation \(\dot H=[H,[H,N]]\), with \([A,B]=AB-BA\), evolving on the space of symmetric matrices. The flow asymptotically diagonalizes symmetric matrices and generalizes the Toda flow. We show that Brockett’s flow can be interpreted as a flow on a flag manifold. In a special case the flow is shown to be equivalent to a Riccati equation.
MSC:
| 93C25 | Control/observation systems in abstract spaces |
References:
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