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...

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...

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

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

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...

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

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...

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...

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

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...

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

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...

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

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 random positioning machine, or RPM, rotates biological samples along two independent axes to change their orientation in space in complex ways and so...

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...

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...

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...

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...

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

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...

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

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

In common usage, randomness is the apparent or actual lack of definite pattern or predictability in information. A random sequence of events, symbols or...

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...

{\displaystyle f(\mathbf {x} )} , where x {\displaystyle \mathbf {x} } is a vector of continuous and/or discrete values. At each iteration, hill climbing will...

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...