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Site updated: 2025-02-07 10:36:17
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htlpt committed Feb 7, 2025
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17 changes: 11 additions & 6 deletions 2021/09/29/What-is-an-RKHS-1/index.html
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<meta property="og:description" content="RKHS随处可见,本系列仅仅为Dino Sejdinovic, Arthur Gretto的What is an RKHS?整理(个人解读+补充)。 第一部分介绍一些必要的泛函的概念。本文中的希尔伯特空间定义使用实数和复数,但是举例仅讨论实数。">
<meta property="og:locale">
<meta property="article:published_time" content="2021-09-29T11:22:37.000Z">
<meta property="article:modified_time" content="2025-02-05T12:06:10.318Z">
<meta property="article:modified_time" content="2025-02-07T02:35:55.218Z">
<meta property="article:author" content="Silven Huang">
<meta property="article:tag" content="functional">
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Expand Down Expand Up @@ -480,13 +480,18 @@ <h3 id="inner-product-内积">Inner product 内积</h3>
<p><span class="math inline">\(\mathcal{F}\)</span>是一个在<span
class="math inline">\(\mathbb{R}\)</span>上的向量空间,函数<span
class="math inline">\(\langle\cdot,\cdot\rangle:\mathcal{F}\times\mathcal{F}\rightarrow\mathbb{R}\)</span><span
class="math inline">\(\mathcal{F}\)</span>上的内积,需满足: - <span
class="math inline">\(\mathcal{F}\)</span>上的内积,需满足:</p>
<ul>
<li><span
class="math inline">\(\langle\alpha_1f_1+\alpha_2f_2,g\rangle_\mathcal{F}:\alpha_1\langle
f_1,g\rangle_\mathcal{F}+\alpha_2\langle
f_2,g\rangle_\mathcal{F}\)</span> - <span class="math inline">\(\langle
f,g\rangle_\mathcal{F}=\langle g,f\rangle_\mathcal{F}\)</span> - <span
class="math inline">\(\langle f,f\rangle_\mathcal{F}\geq 0 \text{ and
}\langle f,f\rangle_\mathcal{F}=0 \text{ iff }f=0\)</span></p>
f_2,g\rangle_\mathcal{F}\)</span></li>
<li><span class="math inline">\(\langle f,g\rangle_\mathcal{F}=\langle
g,f\rangle_\mathcal{F}\)</span></li>
<li><span class="math inline">\(\langle f,f\rangle_\mathcal{F}\geq 0
\text{ and }\langle f,f\rangle_\mathcal{F}=0 \text{ iff
}f=0\)</span></li>
</ul>
<p>可以从内积诱导一个范数<span class="math inline">\(\parallel
f\parallel_\mathcal{F}=\langle f,f\rangle_\mathcal{F}^{1/2}\)</span></p>
<p>内积与范数有一些实用的性质:</p>
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2 changes: 1 addition & 1 deletion css/main.css
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width: 4px;
height: 4px;
border-radius: 50%;
background: #dfc690;
background: #f13778;
}
.links-of-blogroll {
font-size: 13px;
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