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On the matrices of central linear mappings

Hans Havlicek (1996)

Mathematica Bohemica

We show that a central linear mapping of a projectively embedded Euclidean n -space onto a projectively embedded Euclidean m -space is decomposable into a central projection followed by a similarity if, and only if, the least singular value of a certain matrix has multiplicity 2 m - n + 1 . This matrix is arising, by a simple manipulation, from a matrix describing the given mapping in terms of homogeneous Cartesian coordinates.

Optimization of the maximum likelihood estimator for determining the intrinsic dimensionality of high-dimensional data

Rasa Karbauskaitė, Gintautas Dzemyda (2015)

International Journal of Applied Mathematics and Computer Science

One of the problems in the analysis of the set of images of a moving object is to evaluate the degree of freedom of motion and the angle of rotation. Here the intrinsic dimensionality of multidimensional data, characterizing the set of images, can be used. Usually, the image may be represented by a high-dimensional point whose dimensionality depends on the number of pixels in the image. The knowledge of the intrinsic dimensionality of a data set is very useful information in exploratory data analysis,...

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