一个希拉里
发表于 2025-3-21 16:04:38
书目名称Loewner‘s Theorem on Monotone Matrix Functions影响因子(影响力)<br> http://impactfactor.cn/if/?ISSN=BK0587846<br><br> <br><br>书目名称Loewner‘s Theorem on Monotone Matrix Functions影响因子(影响力)学科排名<br> http://impactfactor.cn/ifr/?ISSN=BK0587846<br><br> <br><br>书目名称Loewner‘s Theorem on Monotone Matrix Functions网络公开度<br> http://impactfactor.cn/at/?ISSN=BK0587846<br><br> <br><br>书目名称Loewner‘s Theorem on Monotone Matrix Functions网络公开度学科排名<br> http://impactfactor.cn/atr/?ISSN=BK0587846<br><br> <br><br>书目名称Loewner‘s Theorem on Monotone Matrix Functions被引频次<br> http://impactfactor.cn/tc/?ISSN=BK0587846<br><br> <br><br>书目名称Loewner‘s Theorem on Monotone Matrix Functions被引频次学科排名<br> http://impactfactor.cn/tcr/?ISSN=BK0587846<br><br> <br><br>书目名称Loewner‘s Theorem on Monotone Matrix Functions年度引用<br> http://impactfactor.cn/ii/?ISSN=BK0587846<br><br> <br><br>书目名称Loewner‘s Theorem on Monotone Matrix Functions年度引用学科排名<br> http://impactfactor.cn/iir/?ISSN=BK0587846<br><br> <br><br>书目名称Loewner‘s Theorem on Monotone Matrix Functions读者反馈<br> http://impactfactor.cn/5y/?ISSN=BK0587846<br><br> <br><br>书目名称Loewner‘s Theorem on Monotone Matrix Functions读者反馈学科排名<br> http://impactfactor.cn/5yr/?ISSN=BK0587846<br><br> <br><br>
不能妥协
发表于 2025-3-21 22:35:03
Grundlehren der mathematischen Wissenschaftenhttp://image.papertrans.cn/l/image/587846.jpg
重力
发表于 2025-3-22 04:01:48
Introduction: The Statement of Loewner’s TheoremMost of this monograph will consider finite matrices, but since we will be interested in positivity defined in terms of a (Euclidean) inner product, we make definitions in a general context.
lipoatrophy
发表于 2025-3-22 08:36:05
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Herd-Immunity
发表于 2025-3-22 12:38:21
The Herglotz Representation Theorems and the Easy Direction of Loewner’s TheoremIn this chapter, we will show (b)⇔(c) in Theorems . and . and also (b)⇒(a) and the equivalent part of Theorem .. We’ll have a different proof of (c)⇒(a) in Chapter .. We want to study functions . on . with ., but begin with functions . on . with . and use conformal mapping.
Metastasis
发表于 2025-3-22 14:53:58
Monotonicity of the Square RootAs explained in the preface, most applications of Loewner’s theorem involve the easy half of the theorem. This chapter is an aside involving the two most significant and common matrix monotone functions: fractional powers and the log.
公猪
发表于 2025-3-22 18:46:21
Loewner MatricesIn this chapter, we will reduce matrix monotonicity to the positivity of certain matrices and determinants. Seven of the eleven proofs we’ll give of the hard part of Loewner’s theorem rely on this reduction.
declamation
发表于 2025-3-22 22:55:46
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gregarious
发表于 2025-3-23 04:45:42
In this chapter, we’ll present explicit exampIn this chapter, we’ll present explicit examples that show that . is strictly smaller than . and that show that 2. − 3 in Theorem . is optimal.
单色
发表于 2025-3-23 09:03:43
Heinävaara’s Second Proof of the Dobsch–Donoghue TheoremIn this chapter, we provide a really short, simple, and elegant proof due to Heinävaara of Theorem .. It will be a direct consequence of the mean value theorem for divided differences. Below, . will denote the real polynomials of degree at most ., a real vector space of dimension . + 1.