{"html":"<iframe src=\"https://hatenablog-parts.com/embed?url=https%3A%2F%2Fkazz-scw-2010.hatenablog.com%2Fentry%2F2019%2F03%2F26%2F160952\" title=\"non-degenerate \u306a\u53ef\u5fae\u5206\u5199\u50cf\u306e\u5358\u5c04\u6027 - kazz \u306e\u6570\u5b66\u65c5\u884c\u8a18\" class=\"embed-card embed-blogcard\" scrolling=\"no\" frameborder=\"0\" style=\"display: block; width: 100%; height: 190px; max-width: 500px; margin: 10px 0px;\"></iframe>","title":"non-degenerate \u306a\u53ef\u5fae\u5206\u5199\u50cf\u306e\u5358\u5c04\u6027","version":"1.0","url":"https://kazz-scw-2010.hatenablog.com/entry/2019/03/26/160952","author_url":"https://blog.hatena.ne.jp/kazz-scw/","author_name":"kazz-scw","categories":["\u6570\u5b66\u30a8\u30c3\u30bb\u30fc"],"provider_name":"Hatena Blog","published":"2019-03-26 16:09:52","provider_url":"https://hatena.blog","blog_title":"kazz \u306e\u6570\u5b66\u65c5\u884c\u8a18","image_url":null,"height":"190","blog_url":"https://kazz-scw-2010.hatenablog.com/","width":"100%","description":"\u3042\u308b\u63b2\u793a\u677f\u3067, \u6b21\u306e\u3088\u3046\u306a\u554f\u984c\u3092\u898b\u304b\u3051\u307e\u3057\u305f: f : R^n \u2192 R^n \u304c\u81f3\u308b\u6240\u5fae\u5206\u53ef\u80fd\u3067, \u305d\u306e\u30e4\u30b3\u30d3\u884c\u5217\u5f0f det J(f(x)) \u304c\u81f3\u308b\u6240 \u2260 0 \u306a\u3089\u3070, f \u306f R^n \u4e0a 1-1 \u306b\u306a\u308b\u304b? \u7b54\u3048. n>1 \u3067\u3042\u308c\u3070, \u53cd\u4f8b\u304c\u3042\u308a\u307e\u3059. x = (x_1, ... , x_n) \u2208 R^n \u306b\u5bfe\u3057\u3066, f(x) = f(x_1, ... , x_n) = ( (e^(x_1)) * cos(x_2), (e^(x_1)) * sin(x_2), x_3, .... x_n) \u3068\u304a\u3051\u3070, det J(f(x)) = e^{2x_1}>0 \u3067\u3059\u304c, \u4efb\u610f\u306e (x_1, ... , \u2026","type":"rich"}