Search results
Results from the WOW.Com Content Network
The design matrix has dimension n-by-p, where n is the number of samples observed, and p is the number of variables measured in all samples. [4] [5]In this representation different rows typically represent different repetitions of an experiment, while columns represent different types of data (say, the results from particular probes).
There are two kinds of matrices, viz. a refraction matrix describing the refraction at a lens surface, and a translation matrix, describing the translation of the plane of reference to the next refracting surface, where another refraction matrix applies. The optical system, consisting of a combination of lenses and/or reflective elements, is ...
Moment matrix: Used in statistics and Sum-of-squares optimization: Payoff matrix: A matrix in game theory and economics, that represents the payoffs in a normal form game where players move simultaneously: Pick matrix: A matrix that occurs in the study of analytical interpolation problems: Rotation matrix: A matrix representing a rotation ...
Throughout this article, boldfaced unsubscripted and are used to refer to random vectors, and Roman subscripted and are used to refer to scalar random variables.. If the entries in the column vector = (,, …,) are random variables, each with finite variance and expected value, then the covariance matrix is the matrix whose (,) entry is the covariance [1]: 177 ...
The structure matrix is simply the factor loading matrix as in orthogonal rotation, representing the variance in a measured variable explained by a factor on both a unique and common contributions basis. The pattern matrix, in contrast, contains coefficients which just represent unique contributions. The more factors, the lower the pattern ...
If data generated by a random vector X are observed as vectors X i of observations with covariance matrix Σ, a linear transformation can be used to decorrelate the data. To do this, the Cholesky decomposition is used to express Σ = A A'. Then the transformed vector Y i = A −1 X i has the identity matrix as its covariance matrix.
In probability theory and statistics, the characteristic function of any real-valued random variable completely defines its probability distribution. If a random variable admits a probability density function, then the characteristic function is the Fourier transform (with sign reversal) of the probability density function.
In mathematics, particularly in linear algebra and applications, matrix analysis is the study of matrices and their algebraic properties. [1] Some particular topics out of many include; operations defined on matrices (such as matrix addition, matrix multiplication and operations derived from these), functions of matrices (such as matrix exponentiation and matrix logarithm, and even sines and ...