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In practice, one must be careful to ensure that the resulting covariance matrix (an n × n matrix) is always positive-definite. One strategy is to define a correlation matrix A which is then multiplied by a scalar to give a covariance matrix : this must be positive-definite.
Positive-definite kernels, as defined in (1.1), appeared first in 1909 in a paper on integral equations by James Mercer. [3] Several other authors made use of this concept in the following two decades, but none of them explicitly used kernels K ( x , y ) = f ( x − y ) {\displaystyle K(x,y)=f(x-y)} , i.e. p.d. functions (indeed M. Mathias and ...
The language of mathematics has a wide vocabulary of specialist and technical terms. It also has a certain amount of jargon: commonly used phrases which are part of the culture of mathematics, rather than of the subject.
In mathematics, positive definiteness is a property of any object to which a bilinear form or a sesquilinear form may be naturally associated, which is positive-definite. See, in particular: Positive-definite bilinear form; Positive-definite function; Positive-definite function on a group; Positive-definite functional; Positive-definite kernel
Positive charge, one of the two types of electrical charge; Positive (electrical polarity), in electrical circuits; Positive lens, in optics; Positive (photography), a positive image, in which the color and luminance correlates directly with that in the depicted scene; Positive sense, said of an RNA sequence that codes for a protein
The English language has a number of words that denote specific or approximate quantities that are themselves not numbers. [1] Along with numerals, and special-purpose words like some, any, much, more, every, and all, they are quantifiers. Quantifiers are a kind of determiner and occur in many constructions with other determiners, like articles ...
A thesaurus (pl.: thesauri or thesauruses), sometimes called a synonym dictionary or dictionary of synonyms, is a reference work which arranges words by their meanings (or in simpler terms, a book where one can find different words with similar meanings to other words), [1] [2] sometimes as a hierarchy of broader and narrower terms, sometimes simply as lists of synonyms and antonyms.
The definition of a quantum system includes a complex separable Hilbert space and a set of positive trace-class operators on for which = The set S {\displaystyle {\cal {S}}} is the set of states .
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