MARC details
| 000 -LEADER |
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02490nam a22002657a 4500 |
| 001 - CONTROL NUMBER |
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th521 |
| 003 - CONTROL NUMBER IDENTIFIER |
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ISI Library, Kolkata |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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20240919111719.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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211221b ||||| |||| 00| 0 eng d |
| 040 ## - CATALOGING SOURCE |
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| Original cataloging agency |
ISI Library |
| Language of cataloging |
English |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Edition number |
23 |
| Classification number |
510 |
| Item number |
M678 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Mishra, Hemant Kumar |
| Relator term |
author |
| 245 10 - TITLE STATEMENT |
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| Title |
Differential and subdifferential properties of symplectic eigenvalues/ |
| Statement of responsibility, etc |
Hemant Kumar Mishra |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Place of publication, distribution, etc |
New Delhi: |
| Name of publisher, distributor, etc |
Indian Statistical Institute, |
| Date of publication, distribution, etc |
2021 |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
x,106 pages, |
| 502 ## - DISSERTATION NOTE |
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| Dissertation note |
Thesis (Ph.D.) - Indian Statistical Institute, 2021 |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc |
Includes bibliographical references |
| 505 0# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
Introduction -- 1 Preliminaries -- 2 Differentiability and analyticity of symplectic eigenvalues -- 3 First order directional derivatives of symplectic eigenvalues -- 4 Clarke and Michel-Penot subdifferentials of symplectic eigenvalues -- |
| 508 ## - CREATION/PRODUCTION CREDITS NOTE |
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| Creation/production credits note |
Guided by Prof. Tanvi Jain |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc |
A real 2n × 2n matrix M is called a symplectic matrix if MT JM = J, where J is the<br/>2n × 2n matrix given by J =<br/> O In<br/>−In O<br/><br/>and In is the n × n identity matrix. A result on<br/>symplectic matrices, generally known as Williamson’s theorem, states that for any 2n × 2n<br/>positive definite matrix A there exists a symplectic matrix M such that MT AM = D ⊕ D<br/>where D is an n × n positive diagonal matrix with diagonal entries 0 < d1(A) ≤ · · · ≤ dn(A)<br/>called the symplectic eigenvalues of A. In this thesis, we study differentiability and analyticity<br/>properties of symplectic eigenvalues and corresponding symplectic eigenbasis. In particular,<br/>we prove that simple symplectic eigenvalues are infinitely differentiable and compute their<br/>first order derivative. We also prove that symplectic eigenvalues and corresponding symplectic<br/>eigenbasis for a real analytic curve of positive definite matrices can be chosen real analytically.<br/>We then derive an analogue of Lidskii’s theorem for symplectic eigenvalues as an application<br/>of our analysis. We study various subdifferential properties of symplectic eigenvalues such as<br/>Fenchel subdifferentials, Clarke subdifferentials and Michel-Penot subdifferentials. We show<br/>that symplectic eigenvalues are directionally differentiable and derive the expression of their first order directional derivatives. |
| 650 #4 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Symplectic Eigenvalues |
| 650 #4 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Symplectic Matrix |
| 856 ## - ELECTRONIC LOCATION AND ACCESS |
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| Link text |
Full Text |
| Uniform Resource Identifier |
<a href="http://dspace.isical.ac.in:8080/jspui/handle/10263/7232">http://dspace.isical.ac.in:8080/jspui/handle/10263/7232</a> |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
Dewey Decimal Classification |
| Koha item type |
THESIS |
