LinguisticsLinguistics is the scientific study of language. The modern-day scientific study of linguistics takes all aspects of language into account — i.e., the cognitive, the social, the cultural, the psychological, the environmental, the biological, the literary, the grammatical, the paleographical, and the structural. Linguistics is based on a theoretical as well as descriptive study of language, and is also interlinked with the applied fields of language studies and language learning, which entails the study of specific languages.
Computational linguisticsComputational linguistics has since 2020s became a near-synonym of either natural language processing or language technology, with deep learning approaches, such as large language models, overperforming the specific approaches previously used in the field. The field overlapped with artificial intelligence since the efforts in the United States in the 1950s to use computers to automatically translate texts from foreign languages, particularly Russian scientific journals, into English.
Text corpusIn linguistics and natural language processing, a corpus (: corpora) or text corpus is a dataset, consisting of natively digital and older, digitalized, language resources, either annotated or unannotated. Annotated, they have been used in corpus linguistics for statistical hypothesis testing, checking occurrences or validating linguistic rules within a specific language territory. In search technology, a corpus is the collection of documents which is being searched.
Fréchet spaceIn functional analysis and related areas of mathematics, Fréchet spaces, named after Maurice Fréchet, are special topological vector spaces. They are generalizations of Banach spaces (normed vector spaces that are complete with respect to the metric induced by the norm). All Banach and Hilbert spaces are Fréchet spaces. Spaces of infinitely differentiable functions are typical examples of Fréchet spaces, many of which are typically Banach spaces.
Normed vector spaceIn mathematics, a normed vector space or normed space is a vector space over the real or complex numbers on which a norm is defined. A norm is a generalization of the intuitive notion of "length" in the physical world. If is a vector space over , where is a field equal to or to , then a norm on is a map , typically denoted by , satisfying the following four axioms: Non-negativity: for every ,. Positive definiteness: for every , if and only if is the zero vector.
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