1
Fork 0
mirror of https://github.com/Steffo99/unisteffo.git synced 2024-11-23 00:14:21 +00:00
triennale-appunti-steffo/docs/route-RipassoDiAlgebraLineare.chunk.77c78.js
2020-08-21 18:33:22 +02:00

2 lines
No EOL
12 KiB
JavaScript
Generated

(window.webpackJsonp=window.webpackJsonp||[]).push([[11],{"2w3n":function(r){r.exports={red:"red__2y1B_",orange:"orange__dD2kx",yellow:"yellow__OEpwl",lime:"lime__CVe41",cyan:"cyan__26ZAg",blue:"blue__LO7Xm",magenta:"magenta__1Akee",example:"example__2PzAa"}},U6dl:function(r,o,l){"use strict";l.r(o),function(r){function n(){var r=_(["\frac{Vert x - y Vert}{Vert x Vert}"],["\\frac{\\Vert x - y \\Vert}{\\Vert x \\Vert}"]);return n=function(){return r},r}function e(){var r=_(["Vert x Vert_2 = sqrt{sum_{i = 1}^n x_i^2}"],["\\Vert x \\Vert_2 = \\sqrt{\\sum_{i = 1}^n x_i^2}"]);return e=function(){return r},r}function a(){var r=_(["Vert x Vert_1 = sum_{i = 1}^n | x_i |"],["\\Vert x \\Vert_1 = \\sum_{i = 1}^n | x_i |"]);return a=function(){return r},r}function i(){var r=_(["Vert x Vert_infty = max_{i = 1..n} | x_i |"],["\\Vert x \\Vert_\\infty = max_{i = 1..n} | x_i |"]);return i=function(){return r},r}function t(){var r=_(["\n \begin{pmatrix}\n {color{Gray} 0} & 1 & {color{Gray} 0}\\\n 1 & 1 & {color{Gray} 0}\\\n {color{Gray} 0} & {color{Gray} 0} & 1\n end{pmatrix}\n "],["\n \\begin{pmatrix}\n {\\color{Gray} 0} & 1 & {\\color{Gray} 0}\\\\\n 1 & 1 & {\\color{Gray} 0}\\\\\n {\\color{Gray} 0} & {\\color{Gray} 0} & 1\n \\end{pmatrix}\n "]);return t=function(){return r},r}function c(){var r=_(["A^{-1} cdot A = I"],["A^{-1} \\cdot A = I"]);return c=function(){return r},r}function u(){var r=_(["\n \begin{pmatrix}\n \frac{1}{3} & \frac{2}{3} & -\frac{2}{3}\\\n \frac{2}{3} & \frac{1}{3} & \frac{2}{3}\\\n \frac{2}{3} & -\frac{2}{3} & -\frac{1}{3}\\\n end{pmatrix}\n "],["\n \\begin{pmatrix}\n \\frac{1}{3} & \\frac{2}{3} & -\\frac{2}{3}\\\\\n \\frac{2}{3} & \\frac{1}{3} & \\frac{2}{3}\\\\\n \\frac{2}{3} & -\\frac{2}{3} & -\\frac{1}{3}\\\\\n \\end{pmatrix}\n "]);return u=function(){return r},r}function p(){var r=_(["A^T cdot A = I"],["A^T \\cdot A = I"]);return p=function(){return r},r}function m(){var r=_(["\n \begin{pmatrix}\n {color{Orange} 9} & 1 & 2\\\n 1 & {color{Orange} 8} & 1\\\n 1 & 2 & {color{Orange} 7}\n end{pmatrix}\n "],["\n \\begin{pmatrix}\n {\\color{Orange} 9} & 1 & 2\\\\\n 1 & {\\color{Orange} 8} & 1\\\\\n 1 & 2 & {\\color{Orange} 7}\n \\end{pmatrix}\n "]);return m=function(){return r},r}function d(){var r=_(["\n \begin{pmatrix}\n {color{Gray} 0} & {color{Yellow} -2} & {color{Orange} -4}\\ \n {color{Yellow} 2} & {color{Gray} 0} & {color{Red} -5}\\ \n {color{Orange} 4} & {color{Red} 5} & {color{Gray} 0}\n end{pmatrix}\n "],["\n \\begin{pmatrix}\n {\\color{Gray} 0} & {\\color{Yellow} -2} & {\\color{Orange} -4}\\\\ \n {\\color{Yellow} 2} & {\\color{Gray} 0} & {\\color{Red} -5}\\\\ \n {\\color{Orange} 4} & {\\color{Red} 5} & {\\color{Gray} 0}\n \\end{pmatrix}\n "]);return d=function(){return r},r}function g(){var r=_(["A = -A^T"]);return g=function(){return r},r}function s(){var r=_(["\n \begin{pmatrix}\n 1 & {color{Yellow} 2} & {color{Orange} 4}\\ \n {color{Yellow} 2} & 3 & {color{Red} 5}\\ \n {color{Orange} 4} & {color{Red} 5} & 6\n end{pmatrix}\n "],["\n \\begin{pmatrix}\n 1 & {\\color{Yellow} 2} & {\\color{Orange} 4}\\\\ \n {\\color{Yellow} 2} & 3 & {\\color{Red} 5}\\\\ \n {\\color{Orange} 4} & {\\color{Red} 5} & 6\n \\end{pmatrix}\n "]);return s=function(){return r},r}function f(){var r=_(["A = A^T"]);return f=function(){return r},r}function w(){var r=_(["\n \begin{pmatrix}\n {color{Yellow} 1} & {color{Yellow} 1} & {color{Yellow} 2}\\\n {color{Orange} 2} & {color{Orange} 1} & {color{Orange} 1}\\\n {color{Red} 1} & {color{Red} 2} & {color{Red} 1}\n end{pmatrix}\n "],["\n \\begin{pmatrix}\n {\\color{Yellow} 1} & {\\color{Yellow} 1} & {\\color{Yellow} 2}\\\\\n {\\color{Orange} 2} & {\\color{Orange} 1} & {\\color{Orange} 1}\\\\\n {\\color{Red} 1} & {\\color{Red} 2} & {\\color{Red} 1}\n \\end{pmatrix}\n "]);return w=function(){return r},r}function x(){var r=_(["det(A) \neq 0"],["det(A) \\neq 0"]);return x=function(){return r},r}function Y(){var r=_(["\n \begin{pmatrix}\n {color{Yellow} 3} & {color{Orange} 3} & {color{Orange} 3}\\\n {color{Gray} 0} & {color{Yellow} 4} & {color{Orange} 4}\\\n {color{Gray} 0} & {color{Gray} 0} & {color{Yellow} 5}\n end{pmatrix}\n "],["\n \\begin{pmatrix}\n {\\color{Yellow} 3} & {\\color{Orange} 3} & {\\color{Orange} 3}\\\\\n {\\color{Gray} 0} & {\\color{Yellow} 4} & {\\color{Orange} 4}\\\\\n {\\color{Gray} 0} & {\\color{Gray} 0} & {\\color{Yellow} 5}\n \\end{pmatrix}\n "]);return Y=function(){return r},r}function v(){var r=_(["\n \begin{pmatrix}\n {color{Yellow} 3} & {color{Gray} 0} & {color{Gray} 0}\\\n {color{Orange} 4} & {color{Yellow} 4} & {color{Gray} 0}\\\n {color{Orange} 5} & {color{Orange} 5} & {color{Yellow} 5}\n end{pmatrix}\n "],["\n \\begin{pmatrix}\n {\\color{Yellow} 3} & {\\color{Gray} 0} & {\\color{Gray} 0}\\\\\n {\\color{Orange} 4} & {\\color{Yellow} 4} & {\\color{Gray} 0}\\\\\n {\\color{Orange} 5} & {\\color{Orange} 5} & {\\color{Yellow} 5}\n \\end{pmatrix}\n "]);return v=function(){return r},r}function y(){var r=_(["\n \begin{pmatrix}\n {color{Yellow} 3} & {color{Gray} 0} & {color{Gray} 0}\\\n {color{Gray} 0} & {color{Yellow} 4} & {color{Gray} 0}\\\n {color{Gray} 0} & {color{Gray} 0} & {color{Yellow} 5}\n end{pmatrix}\n "],["\n \\begin{pmatrix}\n {\\color{Yellow} 3} & {\\color{Gray} 0} & {\\color{Gray} 0}\\\\\n {\\color{Gray} 0} & {\\color{Yellow} 4} & {\\color{Gray} 0}\\\\\n {\\color{Gray} 0} & {\\color{Gray} 0} & {\\color{Yellow} 5}\n \\end{pmatrix}\n "]);return y=function(){return r},r}function G(){var r=_(["\n \begin{pmatrix}\n {color{Yellow} 1} & {color{Yellow} 0} & {color{Yellow} 0}\\\n {color{Yellow} 0} & {color{Yellow} 1} & {color{Yellow} 0}\\\n {color{Yellow} 0} & {color{Yellow} 0} & {color{Yellow} 1}\n end{pmatrix}\n "],["\n \\begin{pmatrix}\n {\\color{Yellow} 1} & {\\color{Yellow} 0} & {\\color{Yellow} 0}\\\\\n {\\color{Yellow} 0} & {\\color{Yellow} 1} & {\\color{Yellow} 0}\\\\\n {\\color{Yellow} 0} & {\\color{Yellow} 0} & {\\color{Yellow} 1}\n \\end{pmatrix}\n "]);return G=function(){return r},r}function _(r,o){return o||(o=r.slice(0)),r.raw=o,r}var O=l("mbOI"),b=l("ke5e"),h=String.raw;o.default=function(){return r("div",null,r("h1",null,"Ripasso di ",r("a",{href:"/vldigeometria"},"Algebra Lineare")," ",r("small",null,"per ",r("a",{href:"/calcolonumerico"},"Calcolo Numerico"))),r(O.r,{title:"Matrici speciali"},r(O.q,{title:"Matrice identità"},r("p",null,"Elemento neutro della moltiplicazione matriciale."),r(b.a,null,r(O.p,null,h(G())))),r(O.q,{title:"Matrice diagonale"},r("p",null,"Matrice con elementi diversi da 0 solo sulla diagonale."),r(b.a,null,r(O.p,null,h(y())))),r(O.q,{title:"Matrice triangolare inferiore"},r("p",null,"Matrice con elementi diversi da 0 sopra la diagonale."),r(b.a,null,r(O.p,null,h(v())))),r(O.q,{title:"Matrice triangolare superiore"},r("p",null,"Matrice con elementi diversi da 0 sotto la diagonale."),r(b.a,null,r(O.p,null,h(Y())))),r(O.q,{title:"Matrice non-singolare"},r("p",null,"Matrice con determinante diverso da 0."),r(O.p,null,h(x())),r("p",null,"Sono anche dette ",r("b",null,"matrici linearmente indipendenti")," o ",r("b",null,"matrici invertibili"),"."),r(b.a,null,r(O.p,null,h(w())))),r(O.q,{title:"Matrice simmetrica"},r("p",null,"Matrice con un asse di simmetria lungo la diagonale."),r(O.p,null,h(f())),r(b.a,null,r(O.p,null,h(s())))),r(O.q,{title:"Matrice antisimmetrica"},r("p",null,"Matrice con un asse di simmetria lungo la diagonale; gli elementi nel triangolo superiore sono però l'opposto di quelli del triangolo inferiore."),r("p",null,"Ha sempre degli ",r(O.h,null,"0")," lungo la diagonale."),r(O.p,null,h(g())),r(b.a,null,r(O.p,null,h(d())))),r(O.q,{title:"Matrice a diagonale dominante per riga/colonna"},r("p",null,"Matrice in cui i valori della diagonale sono maggiori della somma di tutti gli altri nella riga/colonna."),r(b.a,null,r(O.p,null,h(m())))),r(O.q,{title:"Matrice ortogonale"},r("p",null,"Matrice che se moltiplicata per la sua trasposta dà come risultato la ",r("b",null,"matrice identità"),"."),r(O.p,null,h(p())),r(b.a,null,r(O.p,null,h(u())))),r(O.q,{title:"Matrice inversa"},r("p",null,"Matrice tale che:"),r(O.p,null,h(c()))),r(O.q,{title:"Matrice sparsa"},r("p",null,"Matrice con pochissimi valori diversi da 0."),r(b.a,null,r(O.p,null,h(t()))))),r(O.r,{title:"Norme"},r(O.q,{title:"Norma vettoriale"},r("p",null,"Funzione che associa un valore positivo a ogni vettore diverso da 0, e 0 al vettore zero."),r(b.a,null,r("a",{href:"https://it.wikipedia.org/wiki/Norma_(matematica)#/media/File:Vector_norms.svg"},"Esempi su Wikipedia"))),r(O.q,{title:"Norma a infinito"},r("p",null,"Massimo dei valori assoluti di tutti gli elementi del vettore."),r("p",null,r(O.h,null,h(i())))),r(O.q,{title:"Norma a 1"},r("p",null,"Somma dei valori assoluti di tutti gli elementi del vettore."),r("p",null,r(O.h,null,h(a())))),r(O.q,{title:"Norma a 2"},r("p",null,"Radice quadrata della somma dei quadrati di tutti gli elementi del vettore."),r("p",null,r(O.h,null,h(e())))),r(O.q,{title:"Errore relativo tra vettori e matrici"},r("p",null,"Le norme sono usate per calcolare l'errore relativo tra due vettori o matrici:"),r("p",null,r(O.h,null,h(n()))))))}}.call(this,l("hosL").h)},ke5e:function(r,o,l){"use strict";(function(r){var n=l("2w3n"),e=l.n(n);o.a=function(o){return r("div",{class:e.a.example},o.children)}}).call(this,l("hosL").h)}}]);
//# sourceMappingURL=route-RipassoDiAlgebraLineare.chunk.77c78.js.map