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Titlebook: Matrix Analysis; Rajendra Bhatia Textbook 1997 Springer-Verlag Berlin Heidelberg 1997 algebra.approximation.calculus.Eigenvalue.exponentia

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發(fā)表于 2025-3-21 16:30:57 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱Matrix Analysis
編輯Rajendra Bhatia
視頻videohttp://file.papertrans.cn/628/627736/627736.mp4
叢書名稱Graduate Texts in Mathematics
圖書封面Titlebook: Matrix Analysis;  Rajendra Bhatia Textbook 1997 Springer-Verlag Berlin Heidelberg 1997 algebra.approximation.calculus.Eigenvalue.exponentia
描述A good part of matrix theory is functional analytic in spirit. This statement can be turned around. There are many problems in operator theory, where most of the complexities and subtleties are present in the finite-dimensional case. My purpose in writing this book is to present a systematic treatment of methods that are useful in the study of such problems. This book is intended for use as a text for upper division and gradu- ate courses. Courses based on parts of the material have been given by me at the Indian Statistical Institute and at the University of Toronto (in collaboration with Chandler Davis). The book should also be useful as a reference for research workers in linear algebra, operator theory, mathe- matical physics and numerical analysis. A possible subtitle of this book could be Matrix Inequalities. A reader who works through the book should expect to become proficient in the art of deriving such inequalities. Other authors have compared this art to that of cutting diamonds. One first has to acquire hard tools and then learn how to use them delicately. The reader is expected to be very thoroughly familiar with basic lin- ear algebra. The standard texts Finite-Dimens
出版日期Textbook 1997
關(guān)鍵詞algebra; approximation; calculus; Eigenvalue; exponential function; inequality; linear algebra; matrices; ma
版次1
doihttps://doi.org/10.1007/978-1-4612-0653-8
isbn_softcover978-1-4612-6857-4
isbn_ebook978-1-4612-0653-8Series ISSN 0072-5285 Series E-ISSN 2197-5612
issn_series 0072-5285
copyrightSpringer-Verlag Berlin Heidelberg 1997
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沙發(fā)
發(fā)表于 2025-3-21 20:27:59 | 只看該作者
Perturbation of Spectral Subspaces of Normal Matrices,their eigenvectors remain stubbornly apart. Note, however, that the . that these two eigenvectors of . and . span are identical. In this chapter we will see that interesting and useful perturbation bounds may be obtained for eigenspaces corresponding to closely bunched eigenvalues of normal matrices.
板凳
發(fā)表于 2025-3-22 02:33:32 | 只看該作者
Spectral Variation of Normal Matrices,orem: if . are two Hermitian matrices, then..In turn, this inequality is a special case of the inequality (IV.62), which says that if Eig↓ (.) denotes the diagonal matrix with entries λ↓. (.) down its diagonal, then we have for all Hermitian matrices . and for all unitarily invariant norms.
地板
發(fā)表于 2025-3-22 06:58:30 | 只看該作者
Spectral Variation of Nonnormal Matrices,quality .(σ(.), σ(.)) ≤ 3|| .|| (Theorem VII.4.1). If one of the matrices . is Hermitian and the other is arbitrary, then we can only have an inequality of the form .(σ(.), σ(.)) ≤ .)||. — B||, where .) is a constant that grows like log . (Problems VI.8.8 and VI.8.9).
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978-1-4612-6857-4Springer-Verlag Berlin Heidelberg 1997
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Matrix Analysis978-1-4612-0653-8Series ISSN 0072-5285 Series E-ISSN 2197-5612
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發(fā)表于 2025-3-23 06:52:06 | 只看該作者
Graduate Texts in Mathematicshttp://image.papertrans.cn/m/image/627736.jpg
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