. "In mathematics, a nonnegative matrix, written is a matrix in which all the elements are equal to or greater than zero, that is, A positive matrix is a matrix in which all the elements are strictly greater than zero. The set of positive matrices is a subset of all non-negative matrices. While such matrices are commonly found, the term is only occasionally used due to the possible confusion with positive-definite matrices, which are different. A matrix which is both non-negative and is positive semidefinite is called a doubly non-negative matrix. A rectangular non-negative matrix can be approximated by a decomposition with two other non-negative matrices via non-negative matrix factorization. Eigenvalues and eigenvectors of square positive matrices are described by the Perron\u2013Frobenius theorem."@en . . "Em matem\u00E1tica, uma matriz n\u00E3o-negativa, escrita como \u00E9 uma matriz na qual todos os elementos s\u00E3o maiores ou iguais a zero, ou seja, Uma matriz positiva \u00E9 uma matriz na qual todos os elementos s\u00E3o estritamente maiores que zero. O conjunto das matrizes positivas \u00E9 um subconjunto de todas as matrizes n\u00E3o-negativas. Enquanto tais matrizes s\u00E3o comumente encontradas, o termo s\u00F3 \u00E9 ocasionalmente usado devido \u00E0 poss\u00EDvel confus\u00E3o com matrizes positiva definidas, que s\u00E3o diferentes. Uma matriz n\u00E3o-negativa retangular pode ser aproximada por uma decomposi\u00E7\u00E3o com duas outras matrizes n\u00E3o-negativas mediante uma . Uma matriz positiva n\u00E3o \u00E9 o mesmo que uma matriz positiva definida. Uma matriz que \u00E9 ao mesmo tempo n\u00E3o-negativa e positive semi-definida \u00E9 denominada matriz duplamente n\u00E3o-negativa. Autovalores e autovetores de matrizes positivas quadradas s\u00E3o descritas pelo teorema de Perron-Frobenius."@pt . . . "Em matem\u00E1tica, uma matriz n\u00E3o-negativa, escrita como \u00E9 uma matriz na qual todos os elementos s\u00E3o maiores ou iguais a zero, ou seja, Uma matriz positiva \u00E9 uma matriz na qual todos os elementos s\u00E3o estritamente maiores que zero. O conjunto das matrizes positivas \u00E9 um subconjunto de todas as matrizes n\u00E3o-negativas. Enquanto tais matrizes s\u00E3o comumente encontradas, o termo s\u00F3 \u00E9 ocasionalmente usado devido \u00E0 poss\u00EDvel confus\u00E3o com matrizes positiva definidas, que s\u00E3o diferentes. Autovalores e autovetores de matrizes positivas quadradas s\u00E3o descritas pelo teorema de Perron-Frobenius."@pt . . . . . . "Matriz n\u00E3o negativa"@pt . . "Inom matematiken \u00E4r en icke-negativ matris en matris d\u00E4r alla element \u00E4r st\u00F6rre \u00E4n eller lika med noll: En positiv matris definieras likartat:"@sv . . . . . . "March 2015"@en . . . "\u6570\u5B66\u306E\u5206\u91CE\u306B\u304A\u3044\u3066\u3001\u975E\u8CA0\u884C\u5217\uFF08\u3072\u3075\u304E\u3087\u3046\u308C\u3064\u3001\u82F1: nonnegative matrix\uFF09\u3068\u306F\u3001\u3059\u3079\u3066\u306E\u6210\u5206\u304C\u30BC\u30ED\u4EE5\u4E0A\u3067\u3042\u308B\u3088\u3046\u306A\u884C\u5217\u3001\u3059\u306A\u308F\u3061 \u3067\u3042\u308B\u3088\u3046\u306A\u884C\u5217\u306E X \u306E\u3053\u3068\u3092\u8A00\u3046\u3002\u6B63\u884C\u5217\uFF08\u305B\u3044\u304E\u3087\u3046\u308C\u3064\u3001positive matrix\uFF09\u3068\u306F\u3001\u3059\u3079\u3066\u306E\u6210\u5206\u304C\u30BC\u30ED\u3088\u308A\u3082\u53B3\u5BC6\u306B\u5927\u304D\u3044\u884C\u5217\u306E\u3053\u3068\u3092\u8A00\u3046\u3002\u6B63\u884C\u5217\u306E\u96C6\u5408\u306F\u3001\u3059\u3079\u3066\u306E\u975E\u8CA0\u884C\u5217\u306E\u96C6\u5408\u306E\u90E8\u5206\u96C6\u5408\u3067\u3042\u308B\u3002 \u30DE\u30EB\u30B3\u30D5\u9023\u9396\u306B\u95A2\u3059\u308B\u9077\u79FB\u884C\u5217\u306F\u3001\u975E\u8CA0\u884C\u5217\u3067\u3042\u308B\u3002 \u9577\u65B9\u5F62\u975E\u8CA0\u884C\u5217\u306F\u3001\u3092\u4ECB\u3057\u305F\u4E8C\u3064\u306E\u7570\u306A\u308B\u975E\u8CA0\u884C\u5217\u306E\u5206\u89E3\u306B\u3088\u3063\u3066\u8FD1\u4F3C\u3059\u308B\u3053\u3068\u304C\u51FA\u6765\u308B\u3002 \u6B63\u884C\u5217\u306F\u3001\u6B63\u5B9A\u5024\u884C\u5217\u3068\u306F\u7570\u306A\u308B\u3002\u975E\u8CA0\u304B\u3064\u6B63\u534A\u5B9A\u5024\u3067\u3042\u308B\u3088\u3046\u306A\u884C\u5217\u306F\u3001\u4E8C\u91CD\u975E\u8CA0\u884C\u5217\uFF08doubly non-negative matrix\uFF09\u3068\u547C\u3070\u308C\u308B\u3002 \u6B63\u306E\u6B63\u65B9\u884C\u5217\u306E\u56FA\u6709\u5024\u3068\u56FA\u6709\u30D9\u30AF\u30C8\u30EB\u306F\u3001\u30DA\u30ED\u30F3\uFF1D\u30D5\u30ED\u30D9\u30CB\u30A6\u30B9\u306E\u5B9A\u7406\u306B\u3088\u3063\u3066\u8868\u73FE\u3055\u308C\u308B\u3002"@ja . "relation to subject of nonnegative matrix not made clear; what is an M-matrix?"@en . . "Matrice \u00E0 coefficients positifs"@fr . "\u6570\u5B66\u306E\u5206\u91CE\u306B\u304A\u3044\u3066\u3001\u975E\u8CA0\u884C\u5217\uFF08\u3072\u3075\u304E\u3087\u3046\u308C\u3064\u3001\u82F1: nonnegative matrix\uFF09\u3068\u306F\u3001\u3059\u3079\u3066\u306E\u6210\u5206\u304C\u30BC\u30ED\u4EE5\u4E0A\u3067\u3042\u308B\u3088\u3046\u306A\u884C\u5217\u3001\u3059\u306A\u308F\u3061 \u3067\u3042\u308B\u3088\u3046\u306A\u884C\u5217\u306E X \u306E\u3053\u3068\u3092\u8A00\u3046\u3002\u6B63\u884C\u5217\uFF08\u305B\u3044\u304E\u3087\u3046\u308C\u3064\u3001positive matrix\uFF09\u3068\u306F\u3001\u3059\u3079\u3066\u306E\u6210\u5206\u304C\u30BC\u30ED\u3088\u308A\u3082\u53B3\u5BC6\u306B\u5927\u304D\u3044\u884C\u5217\u306E\u3053\u3068\u3092\u8A00\u3046\u3002\u6B63\u884C\u5217\u306E\u96C6\u5408\u306F\u3001\u3059\u3079\u3066\u306E\u975E\u8CA0\u884C\u5217\u306E\u96C6\u5408\u306E\u90E8\u5206\u96C6\u5408\u3067\u3042\u308B\u3002 \u30DE\u30EB\u30B3\u30D5\u9023\u9396\u306B\u95A2\u3059\u308B\u9077\u79FB\u884C\u5217\u306F\u3001\u975E\u8CA0\u884C\u5217\u3067\u3042\u308B\u3002 \u9577\u65B9\u5F62\u975E\u8CA0\u884C\u5217\u306F\u3001\u3092\u4ECB\u3057\u305F\u4E8C\u3064\u306E\u7570\u306A\u308B\u975E\u8CA0\u884C\u5217\u306E\u5206\u89E3\u306B\u3088\u3063\u3066\u8FD1\u4F3C\u3059\u308B\u3053\u3068\u304C\u51FA\u6765\u308B\u3002 \u6B63\u884C\u5217\u306F\u3001\u6B63\u5B9A\u5024\u884C\u5217\u3068\u306F\u7570\u306A\u308B\u3002\u975E\u8CA0\u304B\u3064\u6B63\u534A\u5B9A\u5024\u3067\u3042\u308B\u3088\u3046\u306A\u884C\u5217\u306F\u3001\u4E8C\u91CD\u975E\u8CA0\u884C\u5217\uFF08doubly non-negative matrix\uFF09\u3068\u547C\u3070\u308C\u308B\u3002 \u6B63\u306E\u6B63\u65B9\u884C\u5217\u306E\u56FA\u6709\u5024\u3068\u56FA\u6709\u30D9\u30AF\u30C8\u30EB\u306F\u3001\u30DA\u30ED\u30F3\uFF1D\u30D5\u30ED\u30D9\u30CB\u30A6\u30B9\u306E\u5B9A\u7406\u306B\u3088\u3063\u3066\u8868\u73FE\u3055\u308C\u308B\u3002"@ja . . . . . "Une matrice de type est \u00E0 coefficients positifs lorsque tous ses \u00E9l\u00E9ments sont r\u00E9els positifs ; on \u00E9crira alors .Elle est dite strictement positive lorsque tous ses \u00E9l\u00E9ments sont strictement positifs ; on \u00E9crira alors ."@fr . . . . . . . "\u041D\u0435\u043E\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043B\u044C\u043D\u0430\u044F \u043C\u0430\u0442\u0440\u0438\u0446\u0430"@ru . . . . "3713"^^ . . . . "3945884"^^ . . . "Nonnegative matrix"@en . "\u0412 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0435 \u043D\u0435\u043E\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043B\u044C\u043D\u0430\u044F \u043C\u0430\u0442\u0440\u0438\u0446\u0430 \u2014 \u044D\u0442\u043E \u043C\u0430\u0442\u0440\u0438\u0446\u0430, \u044D\u043B\u0435\u043C\u0435\u043D\u0442\u044B \u043A\u043E\u0442\u043E\u0440\u043E\u0439 \u0431\u043E\u043B\u044C\u0448\u0435 \u0438\u043B\u0438 \u0440\u0430\u0432\u043D\u044B \u043D\u0443\u043B\u044E: \u041F\u043E\u043B\u043E\u0436\u0438\u0442\u0435\u043B\u044C\u043D\u0430\u044F \u043C\u0430\u0442\u0440\u0438\u0446\u0430 \u2014 \u044D\u0442\u043E \u043C\u0430\u0442\u0440\u0438\u0446\u0430, \u044D\u043B\u0435\u043C\u0435\u043D\u0442\u044B \u043A\u043E\u0442\u043E\u0440\u043E\u0439 \u0441\u0442\u0440\u043E\u0433\u043E \u0431\u043E\u043B\u044C\u0448\u0435 \u043D\u0443\u043B\u044F: \u041B\u044E\u0431\u0430\u044F \u0441\u0442\u043E\u0445\u0430\u0441\u0442\u0438\u0447\u0435\u0441\u043A\u0430\u044F \u043C\u0430\u0442\u0440\u0438\u0446\u0430 (\u043C\u0430\u0442\u0440\u0438\u0446\u0430 \u043F\u0435\u0440\u0435\u0445\u043E\u0434\u043D\u044B\u0445 \u0432\u0435\u0440\u043E\u044F\u0442\u043D\u043E\u0441\u0442\u0435\u0439 \u0434\u043B\u044F \u0446\u0435\u043F\u0438 \u041C\u0430\u0440\u043A\u043E\u0432\u0430) \u044F\u0432\u043B\u044F\u0435\u0442\u0441\u044F \u043D\u0435\u043E\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043B\u044C\u043D\u043E\u0439. \u041F\u043E\u043B\u043E\u0436\u0438\u0442\u0435\u043B\u044C\u043D\u0443\u044E \u043C\u0430\u0442\u0440\u0438\u0446\u0443 \u043D\u0435 \u0441\u0442\u043E\u0438\u0442 \u043F\u0443\u0442\u0430\u0442\u044C \u0441 \u043F\u043E\u043B\u043E\u0436\u0438\u0442\u0435\u043B\u044C\u043D\u043E \u043E\u043F\u0440\u0435\u0434\u0435\u043B\u0451\u043D\u043D\u043E\u0439 \u043C\u0430\u0442\u0440\u0438\u0446\u0435\u0439. \u041C\u0430\u0442\u0440\u0438\u0446\u0430, \u043A\u043E\u0442\u043E\u0440\u0430\u044F \u043E\u0434\u043D\u043E\u0432\u0440\u0435\u043C\u0435\u043D\u043D\u043E \u044F\u0432\u043B\u044F\u0435\u0442\u0441\u044F \u043D\u0435\u043E\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043B\u044C\u043D\u043E\u0439 \u0438 \u043D\u0435\u043E\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043B\u044C\u043D\u043E \u043E\u043F\u0440\u0435\u0434\u0435\u043B\u0451\u043D\u043D\u043E\u0439, \u043D\u0430\u0437\u044B\u0432\u0430\u044E\u0442 \u0432\u0434\u0432\u043E\u0439\u043D\u0435 \u043D\u0435\u043E\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043B\u044C\u043D\u043E\u0439 \u043C\u0430\u0442\u0440\u0438\u0446\u0435\u0439. \u0421\u043E\u0431\u0441\u0442\u0432\u0435\u043D\u043D\u044B\u0435 \u0437\u043D\u0430\u0447\u0435\u043D\u0438\u044F \u0438 \u0441\u043E\u0431\u0441\u0442\u0432\u0435\u043D\u043D\u044B\u0435 \u0432\u0435\u043A\u0442\u043E\u0440\u0430 \u043A\u0432\u0430\u0434\u0440\u0430\u0442\u043D\u043E\u0439 \u043F\u043E\u043B\u043E\u0436\u0438\u0442\u0435\u043B\u044C\u043D\u043E\u0439 \u043C\u0430\u0442\u0440\u0438\u0446\u044B \u043E\u043F\u0438\u0441\u044B\u0432\u0430\u044E\u0442\u0441\u044F \u0442\u0435\u043E\u0440\u0435\u043C\u043E\u0439 \u0424\u0440\u043E\u0431\u0435\u043D\u0438\u0443\u0441\u0430-\u041F\u0435\u0440\u0440\u043E\u043D\u0430."@ru . . . . "\u0412 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0435 \u043D\u0435\u043E\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043B\u044C\u043D\u0430\u044F \u043C\u0430\u0442\u0440\u0438\u0446\u0430 \u2014 \u044D\u0442\u043E \u043C\u0430\u0442\u0440\u0438\u0446\u0430, \u044D\u043B\u0435\u043C\u0435\u043D\u0442\u044B \u043A\u043E\u0442\u043E\u0440\u043E\u0439 \u0431\u043E\u043B\u044C\u0448\u0435 \u0438\u043B\u0438 \u0440\u0430\u0432\u043D\u044B \u043D\u0443\u043B\u044E: \u041F\u043E\u043B\u043E\u0436\u0438\u0442\u0435\u043B\u044C\u043D\u0430\u044F \u043C\u0430\u0442\u0440\u0438\u0446\u0430 \u2014 \u044D\u0442\u043E \u043C\u0430\u0442\u0440\u0438\u0446\u0430, \u044D\u043B\u0435\u043C\u0435\u043D\u0442\u044B \u043A\u043E\u0442\u043E\u0440\u043E\u0439 \u0441\u0442\u0440\u043E\u0433\u043E \u0431\u043E\u043B\u044C\u0448\u0435 \u043D\u0443\u043B\u044F: \u041B\u044E\u0431\u0430\u044F \u0441\u0442\u043E\u0445\u0430\u0441\u0442\u0438\u0447\u0435\u0441\u043A\u0430\u044F \u043C\u0430\u0442\u0440\u0438\u0446\u0430 (\u043C\u0430\u0442\u0440\u0438\u0446\u0430 \u043F\u0435\u0440\u0435\u0445\u043E\u0434\u043D\u044B\u0445 \u0432\u0435\u0440\u043E\u044F\u0442\u043D\u043E\u0441\u0442\u0435\u0439 \u0434\u043B\u044F \u0446\u0435\u043F\u0438 \u041C\u0430\u0440\u043A\u043E\u0432\u0430) \u044F\u0432\u043B\u044F\u0435\u0442\u0441\u044F \u043D\u0435\u043E\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043B\u044C\u043D\u043E\u0439. \u041F\u043E\u043B\u043E\u0436\u0438\u0442\u0435\u043B\u044C\u043D\u0443\u044E \u043C\u0430\u0442\u0440\u0438\u0446\u0443 \u043D\u0435 \u0441\u0442\u043E\u0438\u0442 \u043F\u0443\u0442\u0430\u0442\u044C \u0441 \u043F\u043E\u043B\u043E\u0436\u0438\u0442\u0435\u043B\u044C\u043D\u043E \u043E\u043F\u0440\u0435\u0434\u0435\u043B\u0451\u043D\u043D\u043E\u0439 \u043C\u0430\u0442\u0440\u0438\u0446\u0435\u0439. \u041C\u0430\u0442\u0440\u0438\u0446\u0430, \u043A\u043E\u0442\u043E\u0440\u0430\u044F \u043E\u0434\u043D\u043E\u0432\u0440\u0435\u043C\u0435\u043D\u043D\u043E \u044F\u0432\u043B\u044F\u0435\u0442\u0441\u044F \u043D\u0435\u043E\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043B\u044C\u043D\u043E\u0439 \u0438 \u043D\u0435\u043E\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043B\u044C\u043D\u043E \u043E\u043F\u0440\u0435\u0434\u0435\u043B\u0451\u043D\u043D\u043E\u0439, \u043D\u0430\u0437\u044B\u0432\u0430\u044E\u0442 \u0432\u0434\u0432\u043E\u0439\u043D\u0435 \u043D\u0435\u043E\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043B\u044C\u043D\u043E\u0439 \u043C\u0430\u0442\u0440\u0438\u0446\u0435\u0439. \u0421\u043E\u0431\u0441\u0442\u0432\u0435\u043D\u043D\u044B\u0435 \u0437\u043D\u0430\u0447\u0435\u043D\u0438\u044F \u0438 \u0441\u043E\u0431\u0441\u0442\u0432\u0435\u043D\u043D\u044B\u0435 \u0432\u0435\u043A\u0442\u043E\u0440\u0430 \u043A\u0432\u0430\u0434\u0440\u0430\u0442\u043D\u043E\u0439 \u043F\u043E\u043B\u043E\u0436\u0438\u0442\u0435\u043B\u044C\u043D\u043E\u0439 \u043C\u0430\u0442\u0440\u0438\u0446\u044B \u043E\u043F\u0438\u0441\u044B\u0432\u0430\u044E\u0442\u0441\u044F \u0442\u0435\u043E\u0440\u0435\u043C\u043E\u0439 \u0424\u0440\u043E\u0431\u0435\u043D\u0438\u0443\u0441\u0430-\u041F\u0435\u0440\u0440\u043E\u043D\u0430."@ru . . "Une matrice de type est \u00E0 coefficients positifs lorsque tous ses \u00E9l\u00E9ments sont r\u00E9els positifs ; on \u00E9crira alors .Elle est dite strictement positive lorsque tous ses \u00E9l\u00E9ments sont strictement positifs ; on \u00E9crira alors ."@fr . . . . . . "1094901435"^^ . "In mathematics, a nonnegative matrix, written is a matrix in which all the elements are equal to or greater than zero, that is, A positive matrix is a matrix in which all the elements are strictly greater than zero. The set of positive matrices is a subset of all non-negative matrices. While such matrices are commonly found, the term is only occasionally used due to the possible confusion with positive-definite matrices, which are different. A matrix which is both non-negative and is positive semidefinite is called a doubly non-negative matrix."@en . "\u975E\u8CA0\u884C\u5217"@ja . "Icke-negativ matris"@sv . . "Inom matematiken \u00E4r en icke-negativ matris en matris d\u00E4r alla element \u00E4r st\u00F6rre \u00E4n eller lika med noll: En positiv matris definieras likartat:"@sv .