{"id":1100,"date":"2023-07-27T16:04:00","date_gmt":"2023-07-27T16:04:00","guid":{"rendered":"https:\/\/statorials.org\/pl\/iloczyn-kropkowy-w-r\/"},"modified":"2023-07-27T16:04:00","modified_gmt":"2023-07-27T16:04:00","slug":"iloczyn-kropkowy-w-r","status":"publish","type":"post","link":"https:\/\/statorials.org\/pl\/iloczyn-kropkowy-w-r\/","title":{"rendered":"Jak obliczy\u0107 iloczyn skalarny w r: z przyk\u0142adami"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Maj\u0105c wektor <em>a<\/em> = [a <sub>1<\/sub> , a <sub>2<\/sub> , a <sub>3<\/sub> ] i wektor <em>b<\/em> = [b <sub>1<\/sub> , b <sub>2<\/sub> , b <sub>3<\/sub> ], <strong>iloczyn skalarny<\/strong> wektora a i wektora b, oznaczony <strong>ab<\/strong> , jest dany wzorem:<\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\"><strong>ab<\/strong> = za <sub>1<\/sub> * b <sub>1<\/sub> + za <sub>2<\/sub> * b <sub>2<\/sub> + za <sub>3<\/sub> * b <sub>3<\/sub><\/span><\/p>\n<p> <span style=\"color: #000000;\">Na przyk\u0142ad, je\u015bli <em>a<\/em> = [2, 5, 6] i <em>b<\/em> = [4, 3, 2], to iloczyn skalarny <em>a<\/em> i <em>b<\/em> b\u0119dzie r\u00f3wny:<\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\"><strong>ab =<\/strong> 2*4 + 5*3 + 6*2<\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\"><strong>ab =<\/strong> 8 + 15 + 12<\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\"><strong>odb =<\/strong> 35<\/span><\/p>\n<p> <span style=\"color: #000000;\">Zasadniczo iloczyn skalarny jest sum\u0105 iloczyn\u00f3w odpowiednich wpis\u00f3w w dw\u00f3ch wektorach.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Jak obliczy\u0107 iloczyn skalarny w R<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Istniej\u0105 dwa sposoby szybkiego obliczenia iloczynu skalarnego dw\u00f3ch wektor\u00f3w w R:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Metoda 1: U\u017cyj %*%<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Poni\u017cszy kod pokazuje, jak u\u017cy\u0107 funkcji <strong>%*%<\/strong> do obliczenia iloczynu skalarnego mi\u0119dzy dwoma wektorami w R:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#definevectors<\/span>\na &lt;- c(2, 5, 6)\nb &lt;- c(4, 3, 2)\n\n<span style=\"color: #008080;\">#calculate dot product between vectors\n<\/span>a %*% b\n\n     [,1]\n[1,] 35<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Iloczyn skalarny okazuje si\u0119 wynosi\u0107 <strong>35<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Nale\u017cy pami\u0119ta\u0107, \u017ce ta funkcja dzia\u0142a r\u00f3wnie\u017c w przypadku kolumn ramki danych:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#define data<\/span>\ndf &lt;- data.frame(a=c(2, 5, 6),\n                 b=c(4, 3, 2))\n\n<span style=\"color: #008080;\">#calculate dot product between columns 'a' and 'b' of data frame\n<\/span>df$a %*% df$b\n\n     [,1]\n[1,] 35<\/strong><\/pre>\n<p> <span style=\"color: #000000;\"><strong>Metoda 2: U\u017cyj funkcji dot().<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Iloczyn skalarny mi\u0119dzy dwoma wektorami mo\u017cemy r\u00f3wnie\u017c obliczy\u0107 za pomoc\u0105 funkcji <strong>dot()<\/strong> z biblioteki <strong>pracma<\/strong> :<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\"><span style=\"color: #000000;\"><span style=\"color: #993300;\">library<\/span> (pracma)<\/span>\n\n#definevectors<\/span>\na &lt;- c(2, 5, 6)\nb &lt;- c(4, 3, 2)\n\n<span style=\"color: #008080;\">#calculate dot product between vectors\n<\/span>dot(a,b)\n\n[1] 35<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Ponownie okazuje si\u0119, \u017ce iloczyn skalarny mi\u0119dzy dwoma wektorami wynosi <strong>35<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Powi\u0105zane:<\/strong> <a href=\"https:\/\/statorials.org\/pl\/produkt-krzyzuje-sie-w-r\/\" target=\"_blank\" rel=\"noopener\">Jak obliczy\u0107 iloczyn krzy\u017cowy w R<\/a><\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Dodatkowe zasoby<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Poni\u017csze samouczki wyja\u015bniaj\u0105, jak obliczy\u0107 iloczyn skalarny za pomoc\u0105 innego oprogramowania statystycznego:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/pl\/jak-\u0142atwo-obliczyc-iloczyn-dote-w-programie-excel\/\" target=\"_blank\" rel=\"noopener noreferrer\">Jak obliczy\u0107 iloczyn skalarny w programie Excel<\/a><br \/> <a href=\"https:\/\/statorials.org\/pl\/kropka-arkusze-google-produktow\/\" target=\"_blank\" rel=\"noopener noreferrer\">Jak obliczy\u0107 iloczyn skalarny w Arkuszach Google<\/a><br \/> <a href=\"https:\/\/statorials.org\/pl\/produkt-kropkowy-ti-84\/\">Jak obliczy\u0107 iloczyn skalarny na kalkulatorze TI-84<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Maj\u0105c wektor a = [a 1 , a 2 , a 3 ] i wektor b = [b 1 , b 2 , b 3 ], iloczyn skalarny wektora a i wektora b, oznaczony ab , jest dany wzorem: ab = za 1 * b 1 + za 2 * b 2 + za 3 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-1100","post","type-post","status-publish","format-standard","hentry","category-przewodnik"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Jak obliczy\u0107 iloczyn skalarny w R (z przyk\u0142adami) - Statoriale<\/title>\n<meta name=\"description\" content=\"W tym samouczku wyja\u015bniono, jak 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