A note on inner-outer factorization of wide matrix-valued functions

A. E. Frazho; A. C.M. Ran

doi:10.1007/978-3-030-04269-1_8

A note on inner-outer factorization of wide matrix-valued functions

A. E. Frazho^*, A. C.M. Ran

^*Corresponding author for this work

Mathematics

Research output: Chapter in Book / Report / Conference proceeding › Chapter › Academic › peer-review

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Abstract

In this paper we expand some of the results of [8, 9, 10]. In fact, using the techniques of [8, 9, 10], we provide formulas for the full rank inner-outer factorization of a wide matrix-valued rational function G with H^∞ entries, that is, functions G with more columns than rows. State space formulas are derived for the inner and outer factor of G.

Original language	English
Title of host publication	Operator Theory, Analysis and the State Space Approach
Subtitle of host publication	In Honor of Rien Kaashoek
Editors	Harm Bart, Sanne ter Horst, André C.M. Ran, Hugo J. Woerdeman
Publisher	Springer International Publishing Switzerland
Pages	201-214
Number of pages	14
ISBN (Electronic)	9783030042691
ISBN (Print)	9783030042684
DOIs	https://doi.org/10.1007/978-3-030-04269-1_8
Publication status	Published - 2018

Publication series

Name	Operator Theory: Advances and Applications
Volume	271
ISSN (Print)	0255-0156
ISSN (Electronic)	2296-4878

Keywords

Inner-outer factorization
Matrix-valued function
State space representation
Toeplitz operators

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10.1007/978-3-030-04269-1_8

Frazho-Ran2018_Chapter_ANoteOnInner-outerFactorizationFinal published version, 346 KBLicence: Article 25fa Dutch Copyright Act

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Frazho, A. E., & Ran, A. C. M. (2018). A note on inner-outer factorization of wide matrix-valued functions. In H. Bart, S. ter Horst, A. C. M. Ran, & H. J. Woerdeman (Eds.), Operator Theory, Analysis and the State Space Approach: In Honor of Rien Kaashoek (pp. 201-214). (Operator Theory: Advances and Applications; Vol. 271). Springer International Publishing Switzerland. https://doi.org/10.1007/978-3-030-04269-1_8

Frazho, A. E. ; Ran, A. C.M. / A note on inner-outer factorization of wide matrix-valued functions. Operator Theory, Analysis and the State Space Approach: In Honor of Rien Kaashoek. editor / Harm Bart ; Sanne ter Horst ; André C.M. Ran ; Hugo J. Woerdeman. Springer International Publishing Switzerland, 2018. pp. 201-214 (Operator Theory: Advances and Applications).

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abstract = "In this paper we expand some of the results of [8, 9, 10]. In fact, using the techniques of [8, 9, 10], we provide formulas for the full rank inner-outer factorization of a wide matrix-valued rational function G with H∞ entries, that is, functions G with more columns than rows. State space formulas are derived for the inner and outer factor of G.",

keywords = "Inner-outer factorization, Matrix-valued function, State space representation, Toeplitz operators",

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Frazho, AE & Ran, ACM 2018, A note on inner-outer factorization of wide matrix-valued functions. in H Bart, S ter Horst, ACM Ran & HJ Woerdeman (eds), Operator Theory, Analysis and the State Space Approach: In Honor of Rien Kaashoek. Operator Theory: Advances and Applications, vol. 271, Springer International Publishing Switzerland, pp. 201-214. https://doi.org/10.1007/978-3-030-04269-1_8

A note on inner-outer factorization of wide matrix-valued functions. / Frazho, A. E.; Ran, A. C.M.
Operator Theory, Analysis and the State Space Approach: In Honor of Rien Kaashoek. ed. / Harm Bart; Sanne ter Horst; André C.M. Ran; Hugo J. Woerdeman. Springer International Publishing Switzerland, 2018. p. 201-214 (Operator Theory: Advances and Applications; Vol. 271).

Research output: Chapter in Book / Report / Conference proceeding › Chapter › Academic › peer-review

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AU - Ran, A. C.M.

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AB - In this paper we expand some of the results of [8, 9, 10]. In fact, using the techniques of [8, 9, 10], we provide formulas for the full rank inner-outer factorization of a wide matrix-valued rational function G with H∞ entries, that is, functions G with more columns than rows. State space formulas are derived for the inner and outer factor of G.

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Frazho AE, Ran ACM. A note on inner-outer factorization of wide matrix-valued functions. In Bart H, ter Horst S, Ran ACM, Woerdeman HJ, editors, Operator Theory, Analysis and the State Space Approach: In Honor of Rien Kaashoek. Springer International Publishing Switzerland. 2018. p. 201-214. (Operator Theory: Advances and Applications). Epub 2018 Dec 31. doi: 10.1007/978-3-030-04269-1_8

A note on inner-outer factorization of wide matrix-valued functions

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