Search results
Results From The WOW.Com Content Network
The factor matrix post-multiplied by its transpose gives the reduced correlation matrix: this is the fundamental factor theorem. The task of factor analysis is to find a factor matrix of the lowest possible rank (the least number of factors) that can reproduce the off-diagonal members of the observed correlation matrix as close as can be ...
In oblique rotation, one may examine both a pattern matrix and a structure matrix. 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 finite element method (FEM) is a powerful technique originally developed for numerical solution of complex problems in structural mechanics, and it remains the method of choice for complex systems. In the FEM, the structural system is modeled by a set of appropriate finite elements interconnected at discrete points called nodes.
Exploratory factor analysis. In multivariate statistics, exploratory factor analysis ( EFA) is a statistical method used to uncover the underlying structure of a relatively large set of variables. EFA is a technique within factor analysis whose overarching goal is to identify the underlying relationships between measured variables. [1]
Low-rank approximation. In mathematics, low-rank approximation is a minimization problem, in which the cost function measures the fit between a given matrix (the data) and an approximating matrix (the optimization variable), subject to a constraint that the approximating matrix has reduced rank. The problem is used for mathematical modeling and ...
Transformation matrix. In linear algebra, linear transformations can be represented by matrices. If is a linear transformation mapping to and is a column vector with entries, then. for some matrix , called the transformation matrix of . [citation needed] Note that has rows and columns, whereas the transformation is from to .
In classical mechanics, a canonical transformation of phase space coordinates is one which preserves the structure of the Poisson brackets. The new variables x',p' have the same Poisson brackets with each other as the original variables x,p. Time evolution is a canonical transformation, since the phase space at any time is just as good a choice ...
In linear algebra, the Cholesky decomposition or Cholesky factorization (pronounced / ʃəˈlɛski / shə-LES-kee) is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful for efficient numerical solutions, e.g., Monte Carlo simulations.