Elementi di teoria delle trasformazioniLA STRUTTURA DI GRUPPOLa struttura di gruppo Un gruppo \303\250 un insieme G in cui \303\250 definita una operazione \302\260 ("leggere tondino")JSFH inoltre \342\210\200 a,b \342\210\210 G allora a \302\260 b \342\210\210 G \342\210\203 1 \342\210\210 G detto elemento neutro tale che \342\210\200a\342\210\210G a\302\2601 = 1\302\260a = a \342\210\200 a\342\210\210 G \342\210\203 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1cEdGJDYlLUkjbWlHRiQ2JlEiYUYnLyUlc2l6ZUdRIzE4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNictSSNtb0dGJDYuUSomdW1pbnVzMDtGJ0YyL0Y5USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZULUkjbW5HRiQ2JVEiMUYnRjJGQUYyRjVGOC8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGQQ== detto inverso di a tale che 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 \342\210\200 a,b,c \342\210\210 G l'operazione \302\260 \303\250 associativa 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Quando l'operazione \342\210\230 \303\250 commutativa si dice che G \303\250 un gruppo abelianoEsempi :1) L'insieme \342\204\232 dei razionali con l'operazione di somma \303\250 un gruppo abeliano in quanto : l'elemento neutro \303\250 lo 0 Se LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkmbWZyYWNHRiQ2KC1JI21pR0YkNiZRIm1GJy8lJXNpemVHUSMxNEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYmLUYvNiZRIm5GJ0YyRjVGOEYyRjVGOC8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGRS8lKWJldmVsbGVkR1EmZmFsc2VGJy9GOVEnbm9ybWFsRic= \303\250 un elemento di \342\204\232 il suo inverso sar\303\240 la frazione 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 la somma \303\250 un'operazione associativa .2) L'insieme \342\204\232 -{0} con l'operazione di prodotto * \303\250 un gruppo abeliano : 1 \303\250 il suo elemento neutro se 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 \303\250 un elemento di \342\204\232 allora LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkmbWZyYWNHRiQ2KC1JI21pR0YkNiZRIm5GJy8lJXNpemVHUSMxNEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYmLUYvNiZRIm1GJ0YyRjVGOEYyRjVGOC8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGRS8lKWJldmVsbGVkR1EmZmFsc2VGJy9GOVEnbm9ybWFsRic= \303\250 il suo inverso il prodotto \303\250 poi associativo3) Il sottoinsieme dei numeri reali della forma 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 (a \342\211\240 0) con l'operazione prodotto \303\250 un gruppo: elemento neutro \303\250 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbW5HRiQ2JVEiMUYnLyUlc2l6ZUdRIzE0RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LlEiK0YnRi9GMi8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOy8lKXN0cmV0Y2h5R0Y7LyUqc3ltbWV0cmljR0Y7LyUobGFyZ2VvcEdGOy8lLm1vdmFibGVsaW1pdHNHRjsvJSdhY2NlbnRHRjsvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZKLUYsNiVRIjBGJ0YvRjItRjY2LlEnJnNkb3Q7RidGL0YyRjlGPEY+RkBGQkZERkYvRklRJjAuMGVtRicvRkxGVC1JJm1zcXJ0R0YkNiMtRiM2JS1GLDYlUSIzRidGL0YyRi9GMkYy l'inverso di a + bLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtc3FydEdGJDYjLUYjNiUtSSNtbkdGJDYlUSIzRicvJSVzaXplR1EjMTRGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGOEY7RjhGOw== \303\250 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUkmbWZyYWNHRiQ2KC1JI21pR0YkNiZRImFGJy8lJXNpemVHUSMxNEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYqLUklbXN1cEdGJDYlRi4tRiM2Ji1JI21uR0YkNiVRIjJGJ0YyL0Y5USdub3JtYWxGJ0YyRjVGOC8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictSSNtb0dGJDYuUSgmbWludXM7RidGMkZGLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZRLyUpc3RyZXRjaHlHRlEvJSpzeW1tZXRyaWNHRlEvJShsYXJnZW9wR0ZRLyUubW92YWJsZWxpbWl0c0dGUS8lJ2FjY2VudEdGUS8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRmpuLUZDNiVRIjNGJ0YyRkYtRkw2LlEnJnNkb3Q7RidGMkZGRk9GUkZURlZGWEZaRmZuL0ZpblEmMC4wZW1GJy9GXG9GZG8tRj42JS1GLzYmUSJiRidGMkY1RjhGQEZIRjJGNUY4LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZgcC8lKWJldmVsbGVkR0ZRLUZMNi5RIn5GJ0YyRkZGT0ZSRlRGVkZYRlpGZm5GY29GZW8tRkw2LlEqJnVtaW51czA7RidGMkZGRk9GUkZURlZGWEZaRmZuRmhuRltvLUYsNihGaG9GO0ZbcEZecEZhcEZjcC1GTDYtRmJvRkZGT0ZSRlRGVkZYRlpGZm5GY29GZW8tSSZtc3FydEdGJDYjLUYjNiQtRkM2JEZfb0ZGRkYtRi82I1EhRidGZnFGZnFGRg== infatti posto 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 l'inverso sar\303\240 il numero 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 tale che 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 Per determinare 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 basta eseguire il prodotto con z ed uguagliare ottenendo il sistema 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print(); # input 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEld2l0aEYnLyUlc2l6ZUdRIzE0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtRiw2JlErU29sdmVUb29sc0YnRi9GMkY1LyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjZRJ25vcm1hbEYnRi9GQy1JI21vR0YkNi5RIjpGJ0YvRkMvJSZmZW5jZUdGQi8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZZRkBGQw==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print(); # input placeholder 4) L'insieme LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEoJiM4NDg0O0YnLyUlc2l6ZUdRIzE0RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYmLUYvNiZRIm1GJ0YyL0Y2USV0cnVlRicvRjlRJ2l0YWxpY0YnRjJGQEZCLyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGOA== degli interi modulo m (con m numero primo) \303\250 un gruppo rispetto alla somma 0 \303\250 l'elemento neutro si indica con -a l'inverso di a rispetto al prodotto LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEoJiM4NDg0O0YnLyUlc2l6ZUdRIzE0RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYmLUYvNiZRIm1GJ0YyL0Y2USV0cnVlRicvRjlRJ2l0YWxpY0YnRjJGQEZCLyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGOA== -{0} \303\250 un gruppo 1 \303\250 l'elemento neutro si indica con 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l'inverso di a ALGEBRA DELLE MATRICI 2X2Una matrice M \303\250 un tabella composta da 4 elementi M= 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Il generico elemento 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 (da leggere l'elemento della riga i-esima e colonna j-esima ) potr\303\240 essere un numero reale anche nullo.La matrice nulla O =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 e la matrice unit\303\240 I = 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 sono primi esempiAd ogni matrice M \303\250 possibile associare un solo numero detto determinante di M e denotato con LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYzLUkjbWlHRiQ2JVEkZGV0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEifkYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZMLUYsNiVRIk1GJ0YvRjJGNS1GNjYtUSI9RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjI3Nzc3NzhlbUYnL0ZORlZGNUY1LUklbXN1YkdGJDYlLUYsNiVRImFGJ0YvRjItRiM2JS1JI21uR0YkNiRRIzExRidGOUYvRjIvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1GNjYtUScmc2RvdDtGJ0Y5RjtGPkZARkJGREZGRkhGSkZNRjUtRlk2JUZlbi1GIzYlLUZbbzYkUSMyMkYnRjlGL0YyRl5vLUY2Ni1RKCZtaW51cztGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GX3AtRlk2JUZlbi1GIzYlLUZbbzYkUSMxMkYnRjlGL0YyRl5vRmFvRjUtRlk2JUZlbi1GIzYlLUZbbzYkUSMyMUYnRjlGL0YyRl5vRjk=Somma di due matrici A e 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= 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di una matrice M per un numero reale k k * 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= 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di una matrice M per un vettore v Prodotto di una matrice M per un vettore 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di due matrici A e 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del prodottoLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=il prodotto non \303\250 commutativo 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per ogni matrice M con det M\342\211\240 0 esiste la matrice inversa 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 tale che 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 dove I \303\250 la matrice unit\303\240L'insieme delle matrici con determinante non nullo formano un gruppo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDRi8= TRASFORMAZIONI AFFINIUna trasformazione geometrica T(x,y) \303\250 una legge matematica che assegna nuove coordinate (x' , y' ) ad un punto a partire da quelle vecchie (x,y)Se \303\250 del tipo 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 con M =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 tale che det M\342\211\2400 parleremo di trasformazione affine ( o di affinit\303\240 )Se det M >0 l'affinit\303\240 sar\303\240 diretta perch\303\250 conserva l'orientamento altrimenti sar\303\240 indiretta e invertir\303\240 l'orientamentoJSFHI coefficienti LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JVEiZUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIn5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1GNjYtUSIsRidGOUY7L0Y/RjFGQEZCRkRGRkZIRkovRk5RLDAuMzMzMzMzM2VtRidGNS1GLDYlUSJmRidGL0YyRjVGOQ== vengono interpretati come componenti di un vettore LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEidkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= ; precisamente LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiZUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= \303\250 la componente orizzontale mentre LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= quella 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 di vettore vEquazioni di una traslazione in forma matriciale 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e in forma semplificata LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzZGLUkjbWlHRiQ2KFEieEYnLyUlc2l6ZUdRIzE4RicvJSVib2xkR1EldHJ1ZUYnLyUnaXRhbGljR0Y0LyUsbWF0aHZhcmlhbnRHUSxib2xkLWl0YWxpY0YnLyUrZm9udHdlaWdodEdRJWJvbGRGJy1JI21vR0YkNjBRIidGJ0YvRjIvRjhGPEY6LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZELyUpc3RyZXRjaHlHRkQvJSpzeW1tZXRyaWNHRkQvJShsYXJnZW9wR0ZELyUubW92YWJsZWxpbWl0c0dGRC8lJ2FjY2VudEdGRC8lJ2xzcGFjZUdRLDAuMTExMTExMWVtRicvJSdyc3BhY2VHUSYwLjBlbUYnLUY+NjBRIn5GJ0YvRjJGQUY6RkJGRUZHRklGS0ZNRk8vRlJGVkZULUY+NjBRIj1GJ0YvRjJGQUY6RkJGRUZHRklGS0ZNRk8vRlJRLDAuMjc3Nzc3OGVtRicvRlVGaW5GV0ZXRitGVy1GPjYwUSIrRidGL0YyRkFGOkZCRkVGR0ZJRktGTUZPL0ZSUSwwLjIyMjIyMjJlbUYnL0ZVRl9vRlctSSVtc3ViR0YkNiUtRiw2KFEidkYnRi9GMkY1RjdGOi1GIzYoRitGL0YyRjVGN0Y6LyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGV0ZXRldGV0ZXRldGV0ZXRldGVy1GLDYoUSJ5RidGL0YyRjVGN0Y6Rj1GV0ZlbkZXRlxwRldGV0Zbb0ZXLUZibzYlRmRvLUYjNihGXHBGL0YyRjVGN0Y6RmlvRi9GMkZBRjo=Una traslazione conserva la distanza tra due puntiLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=TRASFORMAZIONI LINEARI Le equazioni sono della forma ( non vi \303\250 traslazione)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Quindi ogni affinit\303\240 \303\250 la composizione di una trasformazione lineare e una traslazione ISOMETRIE E' una trasformazione affine che conserva la distanza tra due punti . Siano 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 Una generica affinit\303\240 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 li trasformer\303\240 nei punti 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 Vediamo quali sono le condizioni sui coefficienti della matrice affinch\303\251 rimanga invariata la distanza : d(A,B) = d(A' , B') (1)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 La condizione (1) porta alle relazioni 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 Allora scelto un angolo \316\261 e posto LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzZSLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIn5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1GNjYtUSI9RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjI3Nzc3NzhlbUYnL0ZORlNGNS1GLDYlUSRjb3NGJy9GMEY9RjlGNS1GLDYlUScmIzk0NTtGJ0ZYRjlGNUY1RjVGNUY1RjUtRiw2JVEiYkYnRi9GMkZPRjUtRjY2LVEqJnVtaW51czA7RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnL0ZORl1vRjUtRiw2JVEkc2VuRidGL0YyRjVGWUY1RjVGNUY1RjUtRiw2JVEiY0YnRi9GMkZPRjVGVUY1RllGNUY1RjVGNS1GLDYlUSJlRidGL0YyRjVGNS1GLDYlUSJkRidGL0YyRjVGT0Zfb0Y1RllGNUY1Rjk= ( oppure 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 ) possiamo riscrivere la matrice nella forma R(\316\261)= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYoLUYjNiYtSSNtaUdGJDYjUSFGJy1JJ210YWJsZUdGJDY2LUkkbXRyR0YkNictSSRtdGRHRiQ2KC1GIzYkLUYxNiVRK2NvcyZhbHBoYTtGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRkZRJ25vcm1hbEYnLyUpcm93YWxpZ25HRjMvJSxjb2x1bW5hbGlnbkdGMy8lK2dyb3VwYWxpZ25HRjMvJShyb3dzcGFuR1EiMUYnLyUrY29sdW1uc3BhbkdGUi1GOzYoLUYjNiUtSSNtb0dGJDYtUSomdW1pbnVzMDtGJ0ZILyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Zpbi8lKXN0cmV0Y2h5R0Zpbi8lKnN5bW1ldHJpY0dGaW4vJShsYXJnZW9wR0Zpbi8lLm1vdmFibGVsaW1pdHNHRmluLyUnYWNjZW50R0Zpbi8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRmhvLUYxNiVRK3NlbiZhbHBoYTtGJ0ZCRkVGSEZKRkxGTkZQRlNGSkZMRk4tRjg2Jy1GOzYoLUYjNiRGW3BGSEZKRkxGTkZQRlNGOkZKRkxGTi8lJmFsaWduR1ElYXhpc0YnL0ZLUSliYXNlbGluZUYnL0ZNUSdjZW50ZXJGJy9GT1EnfGZybGVmdHxockYnLyUvYWxpZ25tZW50c2NvcGVHRkQvJSxjb2x1bW53aWR0aEdRJWF1dG9GJy8lJndpZHRoR0ZhcS8lK3Jvd3NwYWNpbmdHUSYxLjBleEYnLyUuY29sdW1uc3BhY2luZ0dRJjAuOGVtRicvJSlyb3dsaW5lc0dRJW5vbmVGJy8lLGNvbHVtbmxpbmVzR0Zcci8lJmZyYW1lR0Zcci8lLWZyYW1lc3BhY2luZ0dRLDAuNGVtfjAuNWV4RicvJSplcXVhbHJvd3NHRmluLyUtZXF1YWxjb2x1bW5zR0Zpbi8lLWRpc3BsYXlzdHlsZUdGaW4vJSVzaWRlR1EmcmlnaHRGJy8lMG1pbmxhYmVsc3BhY2luZ0dGaXFGMEZIRkgvSSttc2VtYW50aWNzR0YkUSdNYXRyaXhGJy8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0Zfc0YwRkg= il cui determinante \303\250 1 oppure R'(\316\261)= 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= il cui determinante \303\250 -1 Tali matrici hanno significato di rotazione di angolo \316\261 con centro nell'origine.Le rotazioni R(\316\261) sono un gruppo in cui l'unit\303\240 \303\250 R(0) l'inverso di R(\316\261) \303\250 R(-\316\261) l'operazione di composizione equivale alla rotazione somma degli angoli R(\316\261)\302\260R(\316\262)=R(\316\262+\316\261) in senso antiorarioInfine da quanto visto possiamo dire che nel piano le isometrie sono le affinit\303\240 derivate da composizioni di rotazioni e traslazioni.OMOTETIE E SIMILITUDINIAltre particolari trasformazioni affini sono le OMOTETIE di centro O e rapporto k : A'B' = k ABVediamo come caratterizzare i coefficienti di una matrice lineare affinch\303\251 sia una omotetia.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Siano 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 e 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 i punti immagine nella omotetiaPer definizione dovr\303\240 essere d(A',B') = k d(A , B) 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che porta alle condizioni 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 e alle 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 omotetie con traslazioni otteniamo le SIMILITUDINI (dirette o inverse)LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDgwMjEyMzYyNDE0WColKWFueXRoaW5nRzYiRiVbZ2whIyUhISEiIyIjJiUibUc2JCIiIkYpJkYnNiQiIiNGKUYlTTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDgwMjE4MDMyMjM4WCwlKWFueXRoaW5nRzYiRiVbZ2whIiUhISEjJSIjIiMmJSJtRzYkIiIiRikmRic2JCIiI0YpJkYnNiRGKUYsJkYnNiRGLEYsRiU=