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Symbol b contains −lg(1/4) = 2 bits of information and so it always produces two bits. In contrast, symbol a contains −lg(3/4) ~ 0.415 bits of information, hence sometimes it produces one bit (from state 6 and 7), sometimes 0 bits (from state 4 and 5), only increasing the state, which acts as buffer containing fractional number of bits: lg ...
If S is the set of natural numbers, and T is some subset of the natural numbers, then the indicator vector is naturally a single point in the Cantor space: that is, an infinite sequence of 1's and 0's, indicating membership, or lack thereof, in T. Such vectors commonly occur in the study of arithmetical hierarchy.
In computing, a vector processor or array processor is a central processing unit (CPU) that implements an instruction set where its instructions are designed to operate efficiently and effectively on large one-dimensional arrays of data called vectors.
[3] [4] [5] Geostatistical approaches to multivariate modeling are mostly formulated around the linear model of coregionalization (LMC), a generative approach for developing valid covariance functions that has been used for multivariate regression and in statistics for computer emulation of expensive multivariate computer codes. The ...
Zero-based numbering is a way of numbering in which the initial element of a sequence is assigned the index 0, rather than the index 1 as is typical in everyday non-mathematical or non-programming circumstances.
The vector projection (also known as the vector component or vector resolution) of a vector a on (or onto) a nonzero vector b is the orthogonal projection of a onto a straight line parallel to b. The projection of a onto b is often written as proj b a {\displaystyle \operatorname {proj} _{\mathbf {b} }\mathbf {a} } or a ∥ b .
In vector logic, the matrix-vector structure of logical operators is an exact translation to the format of linear algebra of these Boolean polynomials, where the x and 1−x correspond to vectors s and n respectively (the same for y and 1−y). In the example of NAND, f(1,1)=n and f(1,0)=f(0,1)=f(0,0)=s and the matrix version becomes:
In functional analysis, an F-space is a vector space over the real or complex numbers together with a metric: such that Scalar multiplication in X {\displaystyle X} is continuous with respect to d {\displaystyle d} and the standard metric on R {\displaystyle \mathbb {R} } or C . {\displaystyle \mathbb {C} .}