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A complex vector X ∈ C k is said to be normal if both its real and imaginary components jointly possess a 2k-dimensional multivariate normal distribution. The variance-covariance structure of X is described by two matrices: the variance matrix Γ, and the relation matrix C. Matrix normal distribution describes the case of normally distributed ...
This is a list of Wikipedia articles about curves used in different fields: mathematics ... Rational normal curve; Rose curve; Curves with genus 1 ... Lévy C curve;
This is a gallery of curves used in mathematics, by Wikipedia page. See also list of curves. Algebraic curves. Rational curves. Degree 1. Line. Degree 2 ...
Intuitively, a function is continuous at a point c if the range of f over the neighborhood of c shrinks to a single point () as the width of the neighborhood around c shrinks to zero. More precisely, a function f is continuous at a point c of its domain if, for any neighborhood (()) there is a neighborhood () in its domain such that ...
This can be generalized to restrict the range of values in the dataset between any arbitrary points and , using for example ′ = + (). Note that some other ratios, such as the variance-to-mean ratio ( σ 2 μ ) {\textstyle \left({\frac {\sigma ^{2}}{\mu }}\right)} , are also done for normalization, but are not nondimensional: the units do not ...
This is the meaning of "normal" in the phrases rational normal curve and rational normal scroll. Every regular scheme is normal. Conversely, Zariski (1939, theorem 11) showed that every normal variety is regular outside a subset of codimension at least 2, and a similar result is true for schemes. [1] So, for example, every normal curve is regular.
In mathematics, particularly in operator theory and C*-algebra theory, the continuous functional calculus is a functional calculus which allows the application of a continuous function to normal elements of a C*-algebra. In advanced theory, the applications of this functional calculus are so natural that they are often not even mentioned.
The curl of a vector field F, denoted by curl F, or , or rot F, is an operator that maps C k functions in R 3 to C k−1 functions in R 3, and in particular, it maps continuously differentiable functions R 3 → R 3 to continuous functions R 3 → R 3. It can be defined in several ways, to be mentioned below: