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Generalization of the Concept of Invariance

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Controlled and Conditioned Invariance

Part of the book series: International Centre for Mechanical Sciences ((CISM,volume 109))

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Abstract

Given in Rn a linear transformation represented by the square constant matrix A, and a linear subspace J ⊂ Rn, J is an A-invariant if

(1.1.1)

; A J clearly idicates the transformed of J in the linear transformation A.

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References

  1. Halmos, P.R.: “Finite Dimensional Vector Spaces” Van Nostrand, N.Y., 1958

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  2. Lanczos, C.: “Linear Differential Operators” Van Nostrand, London, 1961

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  3. Basile, G.: “Some Remarks on the Pseudoinverse of a Non-square Matrix” Atti deil’Accademia delle Scienze di Bologna Serie XII, Tomo VI, Anno 257°, 1969

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  4. Basile, G. and Marro, G.: “Controlled and Conditioned Invariant Subspaces in Linear System Theory” Journal of Opt. Th. and Appl. Vol. 3, N° 5, 1969

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  5. Basile, G., Laschi, R. and Marro, G.: “Invarianza controllata e non-interazione nello spazio degli stati” L’Elettrotecnica, N° 1, 1969

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© 1971 Springer-Verlag Wien

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Basile, G. (1971). Generalization of the Concept of Invariance. In: Controlled and Conditioned Invariance. International Centre for Mechanical Sciences, vol 109. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2953-1_2

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  • DOI: https://doi.org/10.1007/978-3-7091-2953-1_2

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-81132-0

  • Online ISBN: 978-3-7091-2953-1

  • eBook Packages: Springer Book Archive

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