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"A base is a natural number B whose powers (B multiplied by itself some number of times) are specially designated within a numerical system." [1]: 38 The term is not equivalent to radix, as it applies to all numerical notation systems (not just positional ones with a radix) and most systems of spoken numbers. [1]
Hexadecimal (also known as base-16 or simply hex) is a positional numeral system that represents numbers using a radix (base) of sixteen. Unlike the decimal system representing numbers using ten symbols, hexadecimal uses sixteen distinct symbols, most often the symbols "0"–"9" to represent values 0 to 9 and "A"–"F" to represent values from ten to fifteen.
In machine learning, the radial basis function kernel, or RBF kernel, is a popular kernel function used in various kernelized learning algorithms. In particular, it is commonly used in support vector machine classification .
In theoretical and computational chemistry, a basis set is a set of functions (called basis functions) that is used to represent the electronic wave function in the Hartree–Fock method or density-functional theory in order to turn the partial differential equations of the model into algebraic equations suitable for efficient implementation on a computer.
The basis of this phenomenon is the entangled states or Bell states of a two qubit system. In this example, Alice and Bob are very far from each other, and have each been given one qubit of the entangled state.
Each Lagrange basis polynomial () can be rewritten as the product of three parts, a function () = common to every basis polynomial, a node-specific constant = (called the barycentric weight), and a part representing the displacement from to : [4]
The exact origins of the LTE lemma are unclear; the result, with its present name and form, has only come into focus within the last 10 to 20 years. [1] However, several key ideas used in its proof were known to Gauss and referenced in his Disquisitiones Arithmeticae. [2]
In this case, the orthonormal basis is sometimes called a Hilbert basis for . Note that an orthonormal basis in this sense is not generally a Hamel basis, since infinite linear combinations are required. [5] Specifically, the linear span of the basis must be dense in , although not necessarily the entire space.