Some Recent Results on Isospectral Flows

The following two results related to recent studies on isospectral flows are presented. (i) The multiple bracket generalizations of Brockett’s dou-ble bracket equation $\dot{H}=[H, [H, N]] $ are proved to have similar properties to Brockett’s equation. (ii) The general formula of isospectral gradient flows, through which we can obtain useful examples, is derived. A new dynamical system which provides a new computational algorithm for solving the eigen-value problem of non-symmetric matrices is calculated as an example.