共查询到20条相似文献，搜索用时 15 毫秒
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Ren-Cang Li. 《Mathematics of Computation》2003,72(242):715-728
This paper continues earlier studies by Bhatia and Li on eigenvalue perturbation theory for diagonalizable matrix pencils having real spectra. A unifying framework for creating crucial perturbation equations is developed. With the help of a recent result on generalized commutators involving unitary matrices, new and much sharper bounds are obtained.
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In this article we focus on perturbation bounds of unitary polar factors in polar decompositions for rectangular matrices. First we present two absolute perturbation bounds in unitarily invariant norms and in spectral norm, respectively, for any rectangular complex matrices, which improve recent results of Li and Sun (SIAM J. Matrix Anal. Appl. 2003; 25 :362–372). Secondly, a new absolute bound for complex matrices of full rank is given. When ‖A ? Ã‖2 ? ‖A ? Ã‖F, our bound for complex matrices is the same as in real case. Finally, some asymptotic bounds given by Mathias (SIAM J. Matrix Anal. Appl. 1993; 14 :588–593) for both real and complex square matrices are generalized. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
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Juan Luo 《Journal of Applied Analysis & Computation》2020,10(3):1107-1117
Let $B$ be a multiplicative perturbation of $Ainmathbb{C}^{mtimes n}$ given by $B=D_1^* A D_2$, where $D_1inmathbb{C}^{mtimes m}$ and $D_2inmathbb{C}^{ntimes n}$ are both nonsingular. New upper bounds for $Vert B^dag-A^dagVert_U$ and $Vert B^dag-A^dagVert_Q$ are derived, where $A^dag,B^dag$ are the Moore-Penrose inverses of $A$ and $B$, and $Vert cdotVert_U,Vert cdotVert_Q$ are any unitarily invariant norm and $Q$-norm, respectively. Numerical examples are provided to illustrate the sharpness of the obtained upper bounds. 相似文献
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本文研究极分解和广义极分解.孙和陈提出的Frobenius范数下的逼近定理被推广至任何酉不变范数情形.得到了次酉极因子的一个新的表达式.通过新的表达式,我们得到了次酉极因子在任何酉不变范数下的扰动界.最后,讨论了数值计算方法. 相似文献
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Hadamard积和酉不变范数不等式 总被引：9，自引：0，他引：9
设Ｍｎ，ｍ是ｎ×ｍ复矩阵空间，Ｍｎ≡Ｍｎ，ｎ．对于Ｈｅｒｍｉｔｅ阵Ｇ，Ｈ∈Ｍｎ，ＧＨ表示Ｇ－Ｈ半正定．记Ａ和Ｂ的Ｈａｄａｍａｒｄ积为ＡＢ．本文证明了若Ａ，Ｂ∈Ｍｎ正定，而Ｘ，Ｙ∈Ｍｎ，ｍ任意，则（ＸＡ－１Ｘ）（ＹＢ－１Ｙ）（ＸＹ）（ＡＢ）－１（ＸＹ），ＸＡ－１Ｘ＋ＹＢ－１Ｙ（Ｘ＋Ｙ）（Ａ＋Ｂ）－１（Ｘ＋Ｙ）．这推广和统一了一些现存的结果．设‖·‖为任意酉不变范数，Ｉ是单位矩阵．本文还证明了对于Ｘ∈Ｍｎ，ｍ和Ａ∈Ｍｎ，Ｂ∈Ｍｍ，若ＡＩ，ＢＩ，则函数ｆ（ｐ）＝‖ＡｐＸ＋ＸＢｐ‖在［０，∞）上单调递增． 相似文献
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AbstractIn various normed spaces we answer the question of when a given isometry is a square of some isometry. In particular, we consider (real and complex) matrix spaces equipped with unitarily invariant norms and unitary congruence invariant norms, as well as some infinite dimensional spaces illustrating the difference between finite and infinite dimensions. 相似文献
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Fuad Kittaneh 《Proceedings of the American Mathematical Society》2002,130(5):1279-1283
Let be a polar decomposition of an complex matrix . Then for every unitarily invariant norm , it is shown that
where denotes the operator norm. This is a quantitative version of the well-known result that is normal if and only if . Related inequalities involving self-commutators are also obtained.
where denotes the operator norm. This is a quantitative version of the well-known result that is normal if and only if . Related inequalities involving self-commutators are also obtained.
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Let r 1, …, r m be positive real numbers and A 1, …, A m be n × n matrices with complex entries. In this article, we present a necessary and sufficient condition for the existence of a unitarily invariant norm ‖·‖, such that ‖A i ‖ = r i , for i = 1, …, m. Then we identify the greatest unitarily invariant norm which satisfies this condition. Using this, we get an approximation of unitarily invariant norms. Although the minimum unitarily invariant norm which satisfies this condition does not exist in general, we find conditions over A i s and r i s which are sufficient for the existence of such a norm. Finally, we get a characterization of unitarily invariant norms. 相似文献
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Dao-sheng Zheng 《计算数学(英文版)》1998,(2)
1.IntroductionSince1984,severalchinesemathematicianshaveobtailledmanyresultsboutmatrixoperatornormcondition.umbe.[ll'12'18].Twokindsmatrixconditionnllmbers[9]are:(1)IfAECoxsisnonsingular,thellunlberK.(A)~IIAll.llA--'if.iscalledtheor--normconditionnumberof… 相似文献
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In this article, we interpolate the well-known Young’s inequality for numbers and matrices, when equipped with the Hilbert–Schmidt norm, then present the corresponding interpolations of recent refinements in the literature. As an application of these interpolated versions, we study the monotonicity these interpolations obey. 相似文献
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B. P. Duggal 《Proceedings of the American Mathematical Society》1998,126(7):2047-2052
Given a Hilbert space , let be operators on . Anderson has proved that if is normal and , then for all operators . Using this inequality, Du Hong-Ke has recently shown that if (instead) , then for all operators . In this note we improve the Du Hong-Ke inequality to for all operators . Indeed, we prove the equivalence of Du Hong-Ke and Anderson inequalities, and show that the Du Hong-Ke inequality holds for unitarily invariant norms.
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Let ‖·‖ be a norm on the algebra ?n of all n × n matrices over ?. An interesting problem in matrix theory is that “Are there two norms ‖·‖1 and ‖·‖2 on ?n such that ‖A‖ = max|‖Ax‖2: ‖x‖1 = 1} for all A ∈ ?n?” We will investigate this problem and its various aspects and will discuss some conditions under which ‖·‖1 = ‖·‖2. 相似文献
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Mitsuru Uchiyama 《Proceedings of the American Mathematical Society》2006,134(5):1405-1412
Let be a nonnegative concave function on with , and let be matrices. Then it is known that , where is the trace norm. We extend this result to all unitarily invariant norms and prove some inequalities of eigenvalue sums.
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Mohammad Al-khlyleh 《Linear and Multilinear Algebra》2017,65(5):922-929
Audenaert recently obtained an inequality for unitarily invariant norms that interpolates between the arithmetic–geometric mean inequality and the Cauchy–Schwarz inequality for matrices. A refined version of Audenaert’s inequality for the Hilbert–Schmidt norm is given. Other interpolating inequalities for unitarily invariant norms are also presented. 相似文献