The coefficients of the field harmonics are obtained from the specific eigen vectors.
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In practice, the covariance ( and sometimes the eigen vectors on this matrix are computed.
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Moreover, the first few eigen vectors can often be interpreted in terms of the large-scale physical behavior of the system.
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Typically, the EOFs are found by computing the eigenvalues and eigen vectors of a spatially weighted anomaly covariance matrix of a field.
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The time series of each mode ( aka, principle components ) are determined by projecting the derived eigen vectors onto the spatially weighted anomalies.
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The eigen vectors that correspond to the largest eigenvalues ( the principal components ) can now be used to reconstruct a large fraction of the variance of the original data.
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To define an absolute score one must normalise the eigen vector e . g . such that the sum over all vertices is 1 or the total number of vertices " n ".
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X " N " eigen value problem ( " N " being the number of data points ), whose bottom " d " nonzero eigen vectors provide an orthogonal set of coordinates.
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The audience for Woodin cardinal will be happy with a higher that that eigen vectors, which will be appropriate at a higher level than triangle or elementary algebra .-- talk ) 00 : 29, 27 September 2006 ( UTC)
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Convolving all the pixels in the image with G, gives orthonormal eigen vectors ? and ? of the J matrix . ? points in the direction of the dominant orientation having the largest contrast and ? points in the direction of the structure orientation having the smallest contrast.
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