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The fundamental idea behind array programming is that operations apply at once to an entire set of values. This makes it a high-level programming model as it allows the programmer to think and operate on whole aggregates of data, without having to resort to explicit loops of individual scalar operations.
R is a programming language for statistical computing and data visualization. It has been adopted in the fields of data mining, bioinformatics and data analysis. [9] The core R language is augmented by a large number of extension packages, containing reusable code, documentation, and sample data. R software is open-source and free software.
For a symmetric matrix A, the vector vec(A) contains more information than is strictly necessary, since the matrix is completely determined by the symmetry together with the lower triangular portion, that is, the n(n + 1)/2 entries on and below the main diagonal. For such matrices, the half-vectorization is sometimes more useful than the ...
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where β is a postulated fixed but unknown vector of k response coefficients, and e is an unknown random vector reflecting random influences on the dependent variable. By some chosen technique such as ordinary least squares , a vector β ^ {\displaystyle {\hat {\beta }}} is chosen as an estimate of β, and the estimate of the vector e , denoted ...
The above defined vector v ∗ ∈ V ∗ is said to be the dual vector of . In an infinite dimensional Hilbert space , analogous results hold by the Riesz representation theorem . There is a mapping V ↦ V ∗ from V into its continuous dual space V ∗ .
A vector database, vector store or vector search engine is a database that can store vectors (fixed-length lists of numbers) along with other data items. Vector databases typically implement one or more Approximate Nearest Neighbor algorithms, [1] [2] [3] so that one can search the database with a query vector to retrieve the closest matching database records.
In computer science and logic, a dependent type is a type whose definition depends on a value. It is an overlapping feature of type theory and type systems.In intuitionistic type theory, dependent types are used to encode logic's quantifiers like "for all" and "there exists".