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Update website

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Steffo 2020-05-01 17:23:38 +02:00
parent 8aabc1b0eb
commit 2ecf22f0ed
24 changed files with 160 additions and 38 deletions

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<!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><title>Appunti Web</title><meta name="viewport" content="width=device-width,initial-scale=1"><meta name="mobile-web-app-capable" content="yes"><meta name="apple-mobile-web-app-capable" content="yes"><link rel="apple-touch-icon" href="./assets/icons/apple-touch-icon.png"><link rel="manifest" href="/manifest.json"><meta name="theme-color" content="#a0ccff"><link rel="shortcut icon" href="/favicon.ico"><style>*{box-sizing:border-box}body{background-color:#0d193b;color:#a0ccff;font-family:sans-serif}</style><link href="/bundle.69171.css" rel="preload" as="style"></head><body><script type="__PREACT_CLI_DATA__">{"preRenderData":{"url":"/"}}</script><script nomodule="">!function(){var e=document,t=e.createElement("script");if(!("noModule"in t)&&"onbeforeload"in t){var n=!1;e.addEventListener("beforeload",function(e){if(e.target===t)n=!0;else if(!e.target.hasAttribute("nomodule")||!n)return;e.preventDefault()},!0),t.type="module",t.src=".",e.head.appendChild(t),t.remove()}}();</script><script crossorigin="anonymous" src="/bundle.6b8a3.esm.js" type="module"></script><script nomodule="" src="/polyfills.b96b2.js"></script><script nomodule="" defer="defer" src="/bundle.109db.js"></script><link rel="stylesheet" href="/bundle.69171.css"></body></html>
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@ -3,6 +3,6 @@ import { Component } from 'preact';
export default class Copyright extends Component {
render() {
return <div class={style.copyright}>© 2019 - Stefano Pigozzi - <a href="https://creativecommons.org/licenses/by-sa/4.0/">CC BY-SA 4.0</a> - <a href="https://github.com/Steffo99/appuntiweb">Codice sorgente</a></div>;
return <div class={style.copyright}>© 2019 - Stefano Pigozzi - <a href="https://creativecommons.org/licenses/by-sa/4.0/">CC BY-SA 4.0</a> - <a href="https://github.com/Steffo99/appuntiweb">Codice sorgente</a> - <a href={"https://ko-fi.com/steffo"}>Supportami</a></div>;
}
}
}

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}
.splitparent {
display: flex;
flex-wrap: wrap;
}
.splitchild {
flex-grow: 1;
flex-shrink: 0;
flex-basis: 0;
}

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@ -202,6 +202,118 @@ export default class CalcoloNumerico extends Component {
</p>
</Panel>
</Split>
<Split title={"Le cose più difficili di Algebra Lineare"}>
<Panel title={"Matrice singolare"}>
<p>
Matrice con determinante 0.
</p>
<p>
Le matrici singolari <b>non sono invertibili</b>.
</p>
</Panel>
</Split>
<Split title={"Norme"}>
<Panel title={"Norma vettoriale"}>
<p>
Funzione che associa un valore positivo a ogni vettore diverso da 0, e 0 al vettore zero.
</p>
<Example>
<a href={"https://it.wikipedia.org/wiki/Norma_(matematica)#/media/File:Vector_norms.svg"}>Esempi su Wikipedia</a>
</Example>
</Panel>
<Panel title={"Norma a infinito"}>
<p>
Massimo dei valori assoluti di tutti gli elementi del vettore.
</p>
<p>
<Latex>{r`\Vert x \Vert_\infty = max_{i = 1..n} | x_i |`}</Latex>
</p>
</Panel>
<Panel title={"Norma a 1"}>
<p>
Somma dei valori assoluti di tutti gli elementi del vettore.
</p>
<p>
<Latex>{r`\Vert x \Vert_1 = \sum_{i = 1}^n | x_i |`}</Latex>
</p>
</Panel>
<Panel title={"Norma a 2"}>
<p>
Radice quadrata della somma dei quadrati di tutti gli elementi del vettore.
</p>
<p>
<Latex>{r`\Vert x \Vert_2 = \sqrt{\sum_{i = 1}^n x_i^2}`}</Latex>
</p>
</Panel>
</Split>
<Split>
<Panel title={"Norma matriciale indotta"}>
<p>
Funzione che associa un valore positivo a ogni matrice diversa da 0, e 0 alla matrice zero.
</p>
<p>
Si ricavano dalle norme vettoriali:
</p>
<p>
<Latex>{r`\Vert A \Vert = sup_{x \in \mathbb{R}, x \neq 0} \frac{\Vert A \cdot x \Vert}{\Vert x \Vert}`}</Latex>
</p>
<Example>
<Latex>sup</Latex> è l'estremo superiore di un insieme. E' molto simile al massimo: ricordi le prime lezioni di Analisi?
</Example>
</Panel>
<Panel title={"Norma a infinito"}>
<p>
Massimo delle somme dei valori assoluti di tutti gli elementi di ogni riga di una matrice.
</p>
<p>
<Latex>{r`\Vert A \Vert_\infty = max_{i = 1..n} \sum_{j = 1}^n | a_{ij} |`}</Latex>
</p>
</Panel>
<Panel title={"Norma a 1"}>
<p>
Massimo delle somme dei valori assoluti di tutti gli elementi di ogni colonna di una matrice.
</p>
<p>
<Latex>{r`\Vert A \Vert_1 = max_{j = 1..n} \sum_{i = 1}^n | a_{ij} |`}</Latex>
</p>
</Panel>
<Panel title={"Norma a 2"}>
<p>
Radice quadrata del rango del prodotto tra una matrice e la sua trasposta.
</p>
<p>
<Latex>{r`\Vert A \Vert_2 = \sqrt{\rho ( A^T \times A ) }`}</Latex>
</p>
</Panel>
</Split>
<Split>
<Panel title={"Errore relativo tra vettori e matrici"}>
<p>
Le norme sono usate per calcolare l'errore relativo tra due vettori o matrici:
</p>
<p>
<Latex>{r`\frac{\Vert x - y \Vert}{\Vert x \Vert}`}</Latex>
</p>
</Panel>
</Split>
<Split title={"Fattorizzazione"}>
<Panel title={"Cos'è?"}>
<p>
La fattorizzazione è il processo che permette di risolvere sistemi di equazioni lineari rappresentati in forma di matrice.
</p>
<p>
Esistono molteplici algoritmi in grado di realizzarla: mentre tutti portano alla stessa soluzione, possono avere <b>velocità</b> e <b>indici algoritmici</b> diversi.
</p>
<p>
Il sistema lineare da risolvere viene diviso in due parti: la <i>matrice dei coefficienti</i> e il <i>vettore termine noto</i>.
</p>
</Panel>
<Panel title={"Teorema di Rouché-Capélli"}>
<p>
</p>
</Panel>
</Split>
</div>
)
}