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  • Eigenvalue, eigenvector and eigenspace — In mathematics, given a linear transformation, an Audio|De eigenvector.ogg|eigenvector of that linear transformation is a nonzero vector which, when that transformation is applied to it, changes in length, but not direction. For each eigenvector… …   Wikipedia

  • Eigenvalues and eigenvectors — For more specific information regarding the eigenvalues and eigenvectors of matrices, see Eigendecomposition of a matrix. In this shear mapping the red arrow changes direction but the blue arrow does not. Therefore the blue arrow is an… …   Wikipedia

  • Principal component analysis — PCA of a multivariate Gaussian distribution centered at (1,3) with a standard deviation of 3 in roughly the (0.878, 0.478) direction and of 1 in the orthogonal direction. The vectors shown are the eigenvectors of the covariance matrix scaled by… …   Wikipedia

  • Principal components analysis — Principal component analysis (PCA) is a vector space transform often used to reduce multidimensional data sets to lower dimensions for analysis. Depending on the field of application, it is also named the discrete Karhunen Loève transform (KLT),… …   Wikipedia

  • Canonical correlation — In statistics, canonical correlation analysis, introduced by Harold Hotelling, is a way of making sense of cross covariance matrices.DefinitionGiven two column vectors X = (x 1, dots, x n) and Y = (y 1, dots, y m) of random variables with finite… …   Wikipedia

  • Matrix mechanics — Quantum mechanics Uncertainty principle …   Wikipedia

  • Diffusion MRI — Diagnostics DTI Color Map MeSH D038524 Diffusion MRI is a mag …   Wikipedia

  • PageRank — is a link analysis algorithm that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of measuring its relative importance within the set. The algorithm may be applied to… …   Wikipedia

  • Vector space — This article is about linear (vector) spaces. For the structure in incidence geometry, see Linear space (geometry). Vector addition and scalar multiplication: a vector v (blue) is added to another vector w (red, upper illustration). Below, w is… …   Wikipedia

  • Modal analysis using FEM — The goal of modal analysis in structural mechanics is to determine the natural mode shapes and frequencies of an object or structure during free vibration. It is common to use the finite element method (FEM) to perform this analysis because, like …   Wikipedia

  • algebra, linear — Introduction       mathematical discipline that deals with vectors (vector) and matrices (matrix) and, more generally, with vector spaces (vector space) and linear transformations. Unlike other parts of mathematics that are frequently invigorated …   Universalium

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