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Biorthogonal decomposition: Difference between revisions
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By multiplying this expression for the covariance matrix ''C'' with the vector φ<sub>k</sub> it is easy to show that the topos φ<sub>k</sub> are the eigenvectors of the covariance matrix ''C'', and λ<sub>k</sub><sup>2</sup> the corresponding eigenvalues. | By multiplying this expression for the covariance matrix ''C'' with the vector φ<sub>k</sub> it is easy to show that the topos φ<sub>k</sub> are the eigenvectors of the covariance matrix ''C'', and λ<sub>k</sub><sup>2</sup> the corresponding eigenvalues. | ||
== Physical interpretation == | |||
For linear systems, the biorthogonal modes converge to the linear eigenmodes of the system in the limit of large ''N''. <ref>[http://dx.doi.org/10.1006/jsvi.2001.3930 G. Kerschen and J. C. Golinval, ''Physical interpretation of the proper orthogonal modes using the Singular Value Decomposition'', Journal of Sound and Vibration '''249''', 5 (2002) 849]</ref> | |||
== See also == | == See also == | ||