Definite
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In grammatical theory, definiteness is a feature of noun phrases, distinguishing between entities which are specific and identifiable in a given context (definite noun phrases) and entities which are not (indefinite noun phrases). There is considerable variation in the expression of definiteness across languages: some languages use a definite article (which can be a free form, a phrasal clitic, or an affix on the noun) to mark a definite noun phrase. Examples are:
Germanic, Romance, Celtic, Semitic, and auxiliary languages generally have a definite article, sometimes used as a postposition. Many other languages do not. Some examples are Chinese, Japanese, Finnish, and the Slavic languages except Bulgarian and Macedonian. When necessary, languages of this kind may indicate definiteness by other means such as Demonstratives. It is common for definiteness to interact with the marking of case in certain syntactic contexts. In many languages direct objects (DOs) receive distinctive marking only if they are definite. For example in Turkish, the DO in the sentence adamları gördüm (meaning "I saw the men") is marked with the suffix -ı (indicating definiteness). The absence of the suffix means that the DO is indefinite ("I saw men"). In Serbo-Croatian (and in the closely-related Baltic languages Latvian and Lithuanian), and to a lesser extent in Slovene, definiteness can be expressed morphologically on prenominal adjectives. The short form of the adjective is interpreted as indefinite (nov grad "a new city"), while the long form is definite and/or specific (novi grad "the new city, a certain new city"). In Japanese, a language which indicates noun functions with postpositions, the topic marker (wa) may include definiteness. For example, 馬は (uma wa) can mean "the horse", while 馬が (uma ga) can mean "a horse". In some languages, the definiteness of the object affects the transitivity of the verb. In the absence of peculiar specificity marking, it also tends to affect the telicity of monooccasional predications. From Wikipedia under the
GNU Free Documentation License Adjectivedefinite (comparative more definite, superlative most definite)
From Wiktionary under the
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Q. I have a matrix K which is symmetric positive definite. I need to normalize the columns of K, that is, Kij = Kij / sum_[i] Kij. This is the same as doing K = KN, where N is a diagonal matrix with entries Nii = 1/sum_[i] Kij. My question is: which matrices K will have a corresponding KN which is still positive definite? Asked by andremsb - Fri Apr 13 11:08:56 2007 - Mathematics - 1 Answers - 3 Comments A. A real symmetric matrix M is positive definite if and only if all the following matrices have a positive determinant (the Sylvester criterion): the upper left 1-by-1 corner of M the upper left 2-by-2 corner of M the upper left 3-by-3 corner of M ... M itself Here, since K is positive definite, the following matrices have a positive determinant: the upper left 1-by-1 corner of K the upper left 2-by-2 corner of K the upper left 3-by-3 corner of K ... K itself Consider L = KN where N is a diagonal matrix. Then det[L] = det[K]*det[N] and it is easy to show that det[upper left i-by-i corner of L] = det[upper left i-by-i corner of K] *det[upper left i-by-i corner of N] for i = 1,2, ... Since det[upper left i-by-i corner of K] > 0 The matrix L… [cont.] Answered by nor^ron - Sat Apr 14 01:44:43 2007 From Yahoo Answer Search: "definite" |
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