statistics, a complex random vector is typically a tuple of complex-valued random variables, and generally is a random variable taking values in a vector space...

{(Z_{n})}\leq \Im {(z_{n})})\end{aligned}}} as definition for the CDS of a complex random vector Z = ( Z 1 , … , Z N ) T {\displaystyle \mathbf {Z} =(Z_{1},\ldots...

that the complex random vector Z = X + i Y {\displaystyle \mathbf {Z} =\mathbf {X} +i\mathbf {Y} \,} is a complex normal random vector or a complex Gaussian...

statistics, complex random variables are a generalization of real-valued random variables to complex numbers, i.e. the possible values a complex random variable...

matrix giving the covariance between each pair of elements of a given random vector. Intuitively, the covariance matrix generalizes the notion of variance...

covariance between the i-th element of a random vector and j-th element of another random vector. When the two random vectors are the same, the cross-covariance...

entries of two random vectors X {\displaystyle \mathbf {X} } and Y {\displaystyle \mathbf {Y} } , while the correlations of a random vector X {\displaystyle...

matrix of two random vectors is a matrix containing as elements the cross-correlations of all pairs of elements of the random vectors. The cross-correlation...

In probability, and statistics, a multivariate random variable or random vector is a list or vector of mathematical variables each of whose value is unknown...

normal distribution to higher dimensions. One definition is that a random vector is said to be k-variate normally distributed if every linear combination...

autocorrelation matrix is a Hermitian matrix for complex random vectors and a symmetric matrix for real random vectors.: p.190  The autocorrelation matrix is a...

Random vector or multivariate random variable, in statistics, a set of real-valued random variables that may be correlated. However, a random vector may...

\operatorname {K} _{\mathbf {X} \mathbf {Y} }} is zero.: p.337  Two complex random vectors Z {\displaystyle \mathbf {Z} } and W {\displaystyle \mathbf {W}...

space) is a real vector space or a complex vector space with an operation called an inner product. The inner product of two vectors in the space is a...

and frames of reference. A basis B of a vector space V over a field F (such as the real numbers R or the complex numbers C) is a linearly independent subset...

of the complex number z {\textstyle z} , If X is a k-dimensional complex random vector, then for t ∈ Ck   φ X ( t ) = E ⁡ [ exp ⁡ ( i Re ⁡ ( t ∗ X ) )...

A vector monitor, vector display, or calligraphic display is a display device used for computer graphics up through the 1970s. It is a type of CRT, similar...

memory slightly. A random vector (that is, a random variable with values in Rn) is said to be a white noise vector or white random vector if its components...

generalizes Gilbert's random graph model, is the random dot-product model. A random dot-product graph associates with each vertex a real vector. The probability...

speed (vector magnitude) will be characterized by a Rayleigh distribution. A second example of the distribution arises in the case of random complex numbers...

probability space is usually referred to as a random variable (or random vector if it takes values in a vector space such as the Banach space B {\displaystyle...

the mean and the covariance matrix of the random vector X {\displaystyle \textstyle \mathbf {X} } , a vector whose jth element ( j = 1 , … , K ) {\displaystyle...

In machine learning, support vector machines (SVMs, also support vector networks) are supervised max-margin models with associated learning algorithms...

can consider random elements of other sets E {\displaystyle E} , such as random Boolean values, categorical values, complex numbers, vectors, matrices,...

collection of random variables is usually called a random field instead. The values of a stochastic process are not always numbers and can be vectors or other...

notice the link between random forest and kernel methods. He pointed out that random forests trained using i.i.d. random vectors in the tree construction...

with it a fixed random n-dimensional unit-length gradient vector, except in the one dimensional case where the gradients are random scalars between −1...

the Fiedler vector. The Fiedler vector can be used to partition a graph. For the example graph in the introductory section, the Fiedler vector is ( 0.415...

represented by capital letters in bold, e.g. A; vectors in lowercase bold, e.g. a; and entries of vectors and matrices are italic (they are numbers from...

sublinear function on a real vector space is symmetric if and only if it is a seminorm. A sublinear function on a real or complex vector space is a seminorm if...