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‎content/posts/cuerpo-total-poem/index.md‎ renamed to ‎content/posts/absoluto-poem/index.md‎

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‎content/posts/caliz-poem/index.md‎

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---
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title: "Poem 8. \"Cáliz\""
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category: personal
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date: 2025-09-21
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---
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```
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te recuerdo en mi sangre,
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calidez que fluye por mi cuello
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derriba mi cabeza;
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te recuerdo en mis lágrimas,
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cierro mis ojos, y te veo
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a través de mis lágrimas;
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siento que te abrazo,
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existes entre mis brazos
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abrazándose a sí mismos,
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siento
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que te cubro de lágrimas,
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siento la calidez
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de tu sangre;
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en mi mente
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te recojo y te defiendo
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del tiempo,
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te junto en un cáliz
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hecho con mis manos,
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que poco a poco
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derrama nuestra sangre,
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derrama nuestras lágrimas
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```

‎content/posts/tensors-signals-kernels/index.md‎

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### Multilinear Algebra
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Perhaps one of the largest contributors to the intellectual moat around topics in machine learning is the concept of a tensor. Besides their typical characterization as "nested arrays," I will provide a perspective that places them in the context of vector spaces and linear maps -- that is, of linear algebra.
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TODO
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#### Vectors and Matrices
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\end{bmatrix}.
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$$
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To talk about multilinear algebra and to gain a principled understanding of tensors, I will expose the idea that $v$ and $M$ are _both_ matrices, each of which simultaneously identifies a vector and a linear map. To tell the complate story behind this, I will establish three resources below and explain afterward.
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To talk about multilinear algebra and to gain a principled understanding of tensors, I will expose the idea that $v$ and $M$ are _both_ matrices, each of which simultaneously identifies a vector and a linear map. For a richer support, I will establish three resources below and explain their relationship afterward.
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{{% hint title="3.8. Remark" %}}
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{{% hint title="3.10. Remark" %}}
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A vector $v \in V$ can be regarded as a linear map from the field $\mathbb{F}$ into $V$, defined by
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A vector $v$ in a space $V$ over $\mathbb{F}$ can be regarded as a linear map from the vector space $\mathbb{F}^1$ into $V$, via
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$$
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\varphi_v : \mathbb{F} \to V, \;\; \varphi_v(\lambda) = \lambda v.
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\varphi_v : \mathbb{F}^1 \to V, \;\; \varphi_v(\lambda) = \lambda v.
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$$
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When a basis for $V$ is fixed, the map $\varphi_v$ is represented by an $n \times 1$ matrix (as an instance of theorem 3.9). This matrix is the familiar column of "coordinates" of $v$.

‎public/index.html‎

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<h3>Personal</h3>
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<ul id="posts">
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<li>
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<a href="http://localhost:1313/poem-8.-c%C3%A1liz/">
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Poem 8. &#34;Cáliz&#34;
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<small><time>Sep 21, 2025</time></small>
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</a>
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</li>
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<li>
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<a href="http://localhost:1313/poem-7.-absoluto/">
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Poem 7. &#34;Absoluto&#34;

‎public/index.xml‎

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<description>Recent content on Max Fierro</description>
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<generator>Hugo -- gohugo.io</generator>
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<language>en-US</language>
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<lastBuildDate>Mon, 15 Sep 2025 00:00:00 +0000</lastBuildDate>
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<lastBuildDate>Sun, 21 Sep 2025 00:00:00 +0000</lastBuildDate>
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<atom:link href="http://localhost:1313/index.xml" rel="self" type="application/rss+xml" />
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<item>
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<title>Poem 8. &#34;Cáliz&#34;</title>
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<link>http://localhost:1313/poem-8.-c%C3%A1liz/</link>
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<pubDate>Sun, 21 Sep 2025 00:00:00 +0000</pubDate>
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<guid>http://localhost:1313/poem-8.-c%C3%A1liz/</guid>
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<description>&lt;pre tabindex=&#34;0&#34;&gt;&lt;code&gt;te recuerdo en mi sangre,
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calidez que fluye por mi cuello
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derriba mi cabeza;
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te recuerdo en mis lágrimas,
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cierro mis ojos, y te veo
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a través de mis lágrimas;
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siento que te abrazo,
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existes entre mis brazos
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abrazándose a sí mismos,
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siento
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que te cubro de lágrimas,
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siento la calidez
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de tu sangre;
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en mi mente
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te recojo y te defiendo
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del tiempo,
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te junto en un cáliz
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hecho con mis manos,
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que poco a poco
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derrama nuestra sangre,
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derrama nuestras lágrimas
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&lt;/code&gt;&lt;/pre&gt;</description>
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</item>
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<item>
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<title>Poem 7. &#34;Absoluto&#34;</title>
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<link>http://localhost:1313/poem-7.-absoluto/</link>

‎public/perspectives-into-tensors-signals-and-kernel-methods/index.html‎

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$$</div>
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</div>
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<h3 id="multilinear-algebra">Multilinear Algebra</h3>
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<p>Perhaps one of the largest contributors to the intellectual moat around topics in machine learning is the concept of a tensor. Besides their typical characterization as &ldquo;nested arrays,&rdquo; I will provide a perspective that places them in the context of vector spaces and linear maps &ndash; that is, of linear algebra.</p>
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<p>TODO</p>
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<h4 id="vectors-and-matrices">Vectors and Matrices</h4>
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<p>A regrettable aspect of a typical introduction to linear algebra is the marriage of syntax to abstract objects. Most of us were told in a first impression that a vector $v$ and a matrix $M$ may look something like this:</p>
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$$
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1 & 2 \\
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3 & 4
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\end{bmatrix}.
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$$<p>To talk about multilinear algebra and to gain a principled understanding of tensors, I will expose the idea that $v$ and $M$ are <em>both</em> matrices, each of which simultaneously identifies a vector and a linear map. To tell the complate story behind this, I will establish three resources below and explain afterward.</p>
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$$<p>To talk about multilinear algebra and to gain a principled understanding of tensors, I will expose the idea that $v$ and $M$ are <em>both</em> matrices, each of which simultaneously identifies a vector and a linear map. For a richer support, I will establish three resources below and explain their relationship afterward.</p>
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<style>
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.box-body > :last-child {
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margin-bottom: 0 !important;
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"
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/>
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<div style="font-size: 0.92em" class="box-body">
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<p>A vector $v \in V$ can be regarded as a linear map from the field $\mathbb{F}$ into $V$, defined by</p>
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<p>A vector $v$ in a space $V$ over $\mathbb{F}$ can be regarded as a linear map from the vector space $\mathbb{F}^1$ into $V$, via</p>
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$$
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\varphi_v : \mathbb{F} \to V, \;\; \varphi_v(\lambda) = \lambda v.
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\varphi_v : \mathbb{F}^1 \to V, \;\; \varphi_v(\lambda) = \lambda v.
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$$<p>When a basis for $V$ is fixed, the map $\varphi_v$ is represented by an $n \times 1$ matrix (as an instance of theorem 3.9). This matrix is the familiar column of &ldquo;coordinates&rdquo; of $v$.</p>
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</div>
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</div>

‎public/poem-7.-cáliz/index.html‎

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<html lang="en"><head><script src="/livereload.js?mindelay=10&amp;v=2&amp;port=1313&amp;path=livereload" data-no-instant defer></script>
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<meta charset="utf-8">
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<meta name="viewport" content="width=device-width, initial-scale=1.0">
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<meta name="description" content="Max&#39;s personal site">
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<link rel="icon" type="image/x-icon" href="/favicon.ico" media="(prefers-color-scheme: light)">
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<link rel="icon" type="image/x-icon" href="/favicon-dark.ico" media="(prefers-color-scheme: dark)">
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<link rel="stylesheet" href="/css/style.min.css">
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<link rel="canonical" href="http://localhost:1313/poem-7.-c%C3%A1liz/" />
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<title>Poem 7. &#34;Cáliz&#34;</title>
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</head>
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<body><header id="banner">
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<a href="http://localhost:1313/"
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><img src="/logo.svg" alt="Logo" class="site-logo"
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/></a>
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<h2><a href="http://localhost:1313/">Max Fierro</a></h2>
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<nav>
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<ul>
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<li>
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<a href="/about/" title="about"
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>about</a
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>
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</li><li>
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<a href="/resume/" title="resume"
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>resume</a
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>
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</li><li>
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<a href="/index.xml" title=""
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>rss</a
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>
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</li>
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</ul>
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</nav>
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</header>
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<main id="content">
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<article>
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<header id="post-header">
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<h1>Poem 7. &#34;Cáliz&#34;</h1>
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<div>
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<time>September 21, 2025</time>
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</div>
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</header><pre tabindex="0"><code>desde ya distantes astros
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por un volumen transparente
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se derrama
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un cuerpo que mi visión sostiene;
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mi mirada atraviesa el cielo
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y se filtra por un medio invisible;
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se somete a su estructura,
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y se concreta,
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se cristaliza:
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si lo busco,
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todo existe en ese cuerpo;
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cada cosa
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es una de sus caras,
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cada perspectiva
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es una de sus esquinas,
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y dentro de su totalidad
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se encuentra a si misma
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mi mirada:
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ser que se yergue
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entre patrones que yo elijo,
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tu cara lo es todo
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y existe en la nada,
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tu mirada me ve
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y me concreta,
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me cristaliza:
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tu mirada se ve a si misma,
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se superpone con la mía,
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cual cristal en simetría;
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y ese encuentro
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brilla como un astro:
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</code></pre></article>
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</main><footer id="footer">
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Copyright © 2024 Max Fierro
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</footer>
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</body>
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</html>

‎public/poem-8.-cáliz/index.html‎

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<html lang="en"><head><script src="/livereload.js?mindelay=10&amp;v=2&amp;port=1313&amp;path=livereload" data-no-instant defer></script>
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<meta charset="utf-8">
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<meta name="viewport" content="width=device-width, initial-scale=1.0">
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<meta name="description" content="Max&#39;s personal site">
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<link rel="icon" type="image/x-icon" href="/favicon.ico" media="(prefers-color-scheme: light)">
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<link rel="icon" type="image/x-icon" href="/favicon-dark.ico" media="(prefers-color-scheme: dark)">
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<link rel="stylesheet" href="/css/style.min.css">
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<link rel="canonical" href="http://localhost:1313/poem-8.-c%C3%A1liz/" />
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<title>Poem 8. &#34;Cáliz&#34;</title>
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</head>
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<body><header id="banner">
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<a href="http://localhost:1313/"
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><img src="/logo.svg" alt="Logo" class="site-logo"
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/></a>
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<h2><a href="http://localhost:1313/">Max Fierro</a></h2>
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<nav>
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<ul>
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<li>
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<a href="/about/" title="about"
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>about</a
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>
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</li><li>
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<a href="/resume/" title="resume"
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>resume</a
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>
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</li><li>
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<a href="/index.xml" title=""
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>rss</a
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>
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</li>
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</ul>
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</nav>
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</header>
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<main id="content">
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<article>
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<header id="post-header">
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<h1>Poem 8. &#34;Cáliz&#34;</h1>
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<div>
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<time>September 21, 2025</time>
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</div>
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</header><pre tabindex="0"><code>te recuerdo en mi sangre,
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calidez que fluye por mi cuello
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derriba mi cabeza;
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te recuerdo en mis lágrimas,
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cierro mis ojos, y te veo
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a través de mis lágrimas;
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siento que te abrazo,
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existes entre mis brazos
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abrazándose a sí mismos,
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siento
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que te cubro de lágrimas,
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siento la calidez
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de tu sangre;
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en mi mente
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te recojo y te defiendo
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del tiempo,
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te junto en un cáliz
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hecho con mis manos,
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que poco a poco
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derrama nuestra sangre,
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derrama nuestras lágrimas
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</code></pre></article>
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</main><footer id="footer">
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Copyright © 2024 Max Fierro
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</footer>
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</body>
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</html>

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