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Topic: Eigenvector

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	Eigenvector Research, Inc.
		Eigenvector Research is pleased to announce our first update to Solo, Solo 4.1.
		Eigenvector is pleased to present Chemometrics for SIMS (Secondary Ion Mass Spectrometry) in Seattle, October 14, 2007.
		Eigenvector Associate Rasmus Bro will lead a series of Chemometrics courses in Sydney, Australia, December 3-7, 2007.
	www.eigenvector.com (993 words)

	Software - Eigenvector Research, Inc.
		Eigenvector Research offers a range of commercial software products.
		Use to test your algorithms or to become familiar with new software with known data.
		The Unscrambler® Accessory Pack for Spectroscopy: Developed jointly by CAMO and Eigenvector Research, this is an add-on to The Unscrambler that includes instrument standardization and orthogonal signal correction.
	software.eigenvector.com (809 words)

	Eigenvectors by Inspection
		An eigenvector of a square matrix M is a nonzero vector v such that
		is an eigenvector of such matrices with associated eigenvalue the constant row sum.
		Finally, for a third eigenvector for F with eigenvalue -1 choose a vector with a nonzero entry in its second column, a 1 in its fourth column, and zeros elsewhere, say
	www.cut-the-knot.org /arithmetic/algebra/eigens.shtml (700 words)

	Eigenvalue, eigenvector and eigenspace - Wikipedia, the free encyclopedia
		In mathematics, and in particular in vector analysis, the eigenvalues, eigenvectors, and eigenspaces of a transformation (from a vector space to itself) are important properties of this transformation.
		A conjugate eigenvector or coneigenvector is a vector sent after transformation to a scalar multiple of its conjugate, where the scalar is called the conjugate eigenvalue or coneigenvalue of the linear transformation.
		In factor analysis, the eigenvectors of a covariance matrix correspond to factors, and eigenvalues to factor loadings.
	en.wikipedia.org /wiki/Eigenvector (4039 words)

	Chapter 6 - Principal Components Analysis Results
		eigenvector then makes up most of the remaining 1% of the variance with the rest of the eigenvectors making up an insignificant part of the variance that appear to be dominated by the noise base on the incoherence of their spectra with wavelength.
		eigenvector would have colder temperature and thus, again, would be in the polar regions and limbs where it would be cold enough to condense clouds and ground frosts.
		Eigenvector 1 seems to indicate a 1-1 correlation with cold regions and frost covered regions which would indicate that the atmosphere of the entire planet has enough water vapor in it that when it gets cold enough it will condense to form clouds of significant optical depth.
	elvis.rowan.edu /~klassen/papers/dissertation/chapter6.htm (2391 words)

	Eigenvector - One Language (Site not responding. Last check: )
		Note that if v is an eigenvector with eigenvalue $c, then any non-zero multiple of v is also an$ eigenvector with eigenvalue $c .$
		In fact, all the eigenvectors with associated eigenvalue $c, together with 0, form a subspace of V, the eigenspace for the eigenvalue c .$
		For example, take the bilateral shift on the Hilbert space $\ell^2(\mathbb{Z}); it is easy to see that any potential$ eigenvector can't be square-summable, so none exist.
	www.onelang.com /encyclopedia/index.php/Eigenvector (900 words)

	PlanetMath: eigenvector (Site not responding. Last check: )
		Of course this is not the smart way to do it; for this, see singular value decomposition.
		This is version 7 of eigenvector, born on 2002-01-19, modified 2004-11-13.
		Object id is 1497, canonical name is Eigenvector.
	planetmath.org /encyclopedia/Eigenvector.html (111 words)

	Gabriel Biplot: Combining subject space and variable space (Site not responding. Last check: )
		You may come across such terms as eigenavlue and eigenvector in factor analysis and principal component analysis (PCA) (Factor analysis and PCA are two different procedures, but most researchers found that they procedure almost identical results on many occasions.
		To understand how eigenvalue and eigenvector work, the data should be considered as a matrix, in which the column vector represents the subject space while the row vector represents the variable space.
		Eigenvectors and Eigenvalues can be used in regression diagnosis and principle component analysis.
	seamonkey.ed.asu.edu /~alex/computer/sas/biplot.html (2264 words)

	Eigenvectors and eigenvalues (Site not responding. Last check: )
		Eigenvectors and eigenvalues are important in physics for many reasons.
		An entirely different way that eigenvectors arise is in the theory of systems of differential equations, such as the equations which relate two populations, which we can think of as prey and predators.
		One of the uses of eigenvectors is to simplify a matrix by the process of diagonalization.
	www.mathphysics.com /calc/eigen.html (3253 words)

	eigenvector (Site not responding. Last check: )
		The scalar in question is called the eigenvalue corresponding to this eigenvector.
		An important theorem says, roughly, that certain linear transformations have enough eigenvectors that they form a basis of the whole vector states.
		An eigenvector is a (representative member of a) fixed point of the map on the projective plane induced by a linear map.
	www.linuxguruz.com /foldoc/foldoc.php?eigenvector (199 words)

	Eigenvalues and Eigenvectors
		Definition 9.2 The dominant eigenvector of a matrix is an eigenvector corresponding to the eigenvalue of largest magnitude (for real numbers, largest absolute value) of that matrix.
		Remark 29 Because any constant multiple of an eigenvector is an eigenvector, we did not have to divide by the last element in the vector in step 3.
		= 0 is an eigenvector corresponding to the eigenvalue
	ceee.rice.edu /Books/LA/eigen (2757 words)

	sciforums.com - Eigenvalue & Eigenvector
		When you calculate all possible eigenvalues of H you know all the allowed energy levels of that particle (this is a way to explain atomic spectra: an allowed energylevel is simply an eigenvalue of the energy-matrix).
		An example: If you measure the energy, and you get E as a result (remember this is an eigenvalue for the energy-matrix, with some eigenvector belonging to it)...
		The entire set of particles is a lot more than the sum of the individual particles in quantum mechanics (but this is even true in classical mechanics, but that's a different story).
	www.sciforums.com /printthread.php?t=17720 (517 words)

	Method and apparatus for ranking web page search results - US Patent 6871202 (Site not responding. Last check: )
		The matrix L has a principal eigenvector which corresponds to the eigenvalue of highest magnitude of the matrix that can be determined using one of several known suitable numerical methods.
		The quality of the page corresponds to the eigenvector number for the page, i.e., the higher the value of the eigenvector coefficient, the more useful the site is likely to be in terms of the quality being sought.
		Notably, other eigenvectors beside the principle eigenvector can also be used to rank the pages, instead of or in addition to, the ranking achieved with the principle eigenvector.
	www.patentstorm.us /patents/6871202.html (4990 words)

	Eigenvector-Following Transition State Searches (Site not responding. Last check: )
		We count up from the eigenvector corresponding to the smallest eigenvalue, the one corresponding to the second smallest eigenvalue etc.
		The value specified by MODE is only effective on the first step: for subsequent steps the critical eigenvector is chosen by a maximum overlap criterion using the dot product with the eigenvector that was followed at the previous step.
		The chosen eigenvector is simply set to the same one that was followed in the last step, where the eigenvectors are numbered in terms of the corresponding eigenvalues arranged in ascending order.
	brian.ch.cam.ac.uk /~wales/OPTIM/node34.html (209 words)

	Eigenvalues and Eigenvectors of a Matrix
		As the null vector is an eigenvector for every square matrix A in eigenvalues problem (6), in following we will confine ourselves to the non-trivial eigenvectors.
		is an eigenvector of the matrix A corresponding to the eigenvalue
		The eigenvectors of the matrix A corresponding to the different eigenvalues are linearly independent.
	www.cs.ut.ee /~toomas_l/linalg/lin1/node16.html (955 words)

	eigenvector (Site not responding. Last check: )
		Peres-Neto, P.R., Jackson, D.A. and Somers K.M. Assessing the significance of eigenvector coefficients in principal component analysis.
		In this study we compared the performance of a variety of approaches for assessing the significance of eigenvector coefficients in terms of type I error rates and power.
		We used a variety of simulated scenarios to examine the influence of the number of real dimensions in the data; unique versus complex variables; the magnitude of eigenvector coefficients; and the number of variables associated with a particular dimension.
	www.zoo.utoronto.ca /pperes/eigenvector.html (232 words)

	ACD/Labs and Eigenvector Provide Enhanced Toolset Integration
		Eigenvector created the DataSet object as a tool to facilitate data set handling within MATLAB™, and to enhance the exchange and translation of complete data sets between file types.
		Eigenvector Research, Inc. (EVRI) is a Chemometrics Research and Applications Company located in Manson, Washington, USA.
		With an experienced staff, Eigenvector Research is well prepared to apply modern multivariate statistical methods to your data while keeping a firm grasp of the underlying chemical aspects of the system.
	www.acdlabs.co.uk /clients/pr_eigenvector0704.html (599 words)

	ACD/Labs and Eigenvector Provide Enhanced Toolset Integration
		Eigenvector created the DataSet object as a tool to facilitate data set handling within MATLAB™, and to enhance the exchange and translation of complete data sets between file types.
		Eigenvector Research, Inc. (EVRI) is a Chemometrics Research and Applications Company located in Manson, Washington, USA.
		With an experienced staff, Eigenvector Research is well prepared to apply modern multivariate statistical methods to your data while keeping a firm grasp of the underlying chemical aspects of the system.
	www.acdlabs.com /clients/pr_eigenvector0704.html (599 words)

	Algebra:Eigenvalues and eigenvectors - Wikibooks
		Eigenvalues and eigenvectors are related to fundamental properties of matrices.
		We usually choose an eigenvector for some convenience such as "most whole number entries", "first entry is 1", or "length of the eigenvector is 1".
		Eigenvalues and eigenvectors are not mere pretty facts about these vectors; they have relevant and important applications.
	en.wikibooks.org /wiki/Algebra:Eigenvalues_and_eigenvectors (1239 words)

	eigenvector - OneLook Dictionary Search
		Tip: Click on the first link on a line below to go directly to a page where "eigenvector" is defined.
		Eigenvector : A Glossary of Mathematical Terms [home, info]
		Eigenvector : The Computational Beauty of Nature [home, info]
	www.onelook.com /cgi-bin/cgiwrap/bware/dofind.cgi?word=eigenvector (133 words)

	15.13. Eigenvalue and Eigenvector Extraction (Site not responding. Last check: )
		The eigenvectors associated with multiple eigenvalues are evaluated using initial vector deflation by Gram-Schmidt orthogonalization in the inverse iteration procedure.
		The eigenvalues and eigenvectors of Equation 15.158 and Equation 15.159 are related by:
		The transformed problem is given by Equation 15.159 and from there on, the eigenvalues and eigenvectors computation follow along the same lines as for the unsymmetric eigensolver.
	www.oulu.fi /atkk/tkpalv/unix/ansys-6.1/content/thy_tool13.html (2420 words)

	Problem #5 (Site not responding. Last check: )
		Since our most important eigenvector is the one with the largest eigenvalue, I switched the order here.
		Hence, the first eigenvector shown is the image "hw5_eig256" which is the plot of E(:,256).
		As we move on, the eigenvectors appear to be more and more varied.
	www.math.umn.edu /~wittman/hw1_p5.html (136 words)

	Eigenvector : Eigenvalue (Site not responding. Last check: )
		In linear algebra, the eigenvectors (from the German eigen meaning "own") of a linear operator are non-zero vectors which, when operated on by the operator, result in a scalar multiple of themselves.
		scaling: all vectors are eigenvectors, and the eigenvalue is the scale factor
		An important tool for describing eigenvalues of square matrices is the characteristic polynomial: saying that c is an eigenvalue of A is equivalent to stating that the system of linear equations (A - cI) x
	www.city-search.org /ei/eigenvalue.html (1083 words)

	Initial eigenvector guesses
		This section deals with the various ways of generating initial sets of eigenvectors, and altering the order of the orbitals.
		There is a default mechanism for generating the initial guess, which will be described shortly, but the commands most likely to be used are those for altering the order of the orbitals, and for locking the orbitals into a particular order, so this will be dealt with first.
		If you wish to use GUESS RESTORE to transfer eigenvectors from one job to another, you should first copy the file which was the dumpfile (ie ED3 = fort.14) to another file which is not going to be in use.
	www-theor.ch.cam.ac.uk /software/cadpac/chap2/node22.html (1403 words)

	Eigenvector Demo (Site not responding. Last check: )
		An eigenvector v of a matrix A satisfies the following equation: Av=cv where c is a scalar, actually c is the eigenvalue of the matrix A.
		If a matrix has an eigenvector, then it has an infinite number of them.
		To see this, simply take your original vector v and multiply it by any scalar you want (rather lengthen or shorten your vector v on the screen), this is another eigenvector.
	www.math.ucla.edu /~baker/java/hoefer/Eigendemo.htm (178 words)

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