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A special property of the matrix Riccati equation

Published online by Cambridge University Press:  17 April 2009

A.N. Stokes
A.N. Stokes
Affiliation:
Division of Environmental Mechanics, CSIRO, Canberra, ACT.
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In the domain of real symmetric matrices ordered by the positive definiteness criterion, the symmetric matrix Riccati differential equation has the unusual property of preserving the ordering of its solutions as the independent variable changes, Here is is shown that, subject to a continuity restriction, the Riccati equation is unique among comparable equations in possessing this property.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 10 , Issue 2 , April 1974 , pp. 245 - 253
Copyright
Copyright © Australian Mathematical Society 1974

References

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