Differential geometry of a parametric family of invertible linear systems—Riemannian metric, dual affine connections, and divergence

DOI10.1007/BF01692059zbMath0632.93017OpenAlexW1994796137WikidataQ115393223 ScholiaQ115393223MaRDI QIDQ3770366

Shun-ichi Amari

Publication date: 1987

Published in: Mathematical Systems Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01692059

zbMATH Keywords

Riemannian metricgeodesicsHilbert manifoldconnectionsdivergencespectral densityorder reductiontime-invariantapproximation problemstochastic realizationdifferential-geometric statisticslinear, discrete-time control systems

Mathematics Subject Classification ID

Gaussian processes (60G15) Discrete-time control/observation systems (93C55) Geometric methods (93B27) Linear systems in control theory (93C05) Identification in stochastic control theory (93E12) Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20) Geodesics in global differential geometry (53C22) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Realizations from input-output data (93B15) Connections (general theory) (53C05)

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