On the Matrices of Central Linear Mappings

zbMATH Open0863.51020arXiv1210.1922MaRDI QIDQ3128575

H. Havlicek

Publication date: 17 April 1997

Abstract: 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 $ge2m-n+1$. This matrix is arising, by a simple manipulation, from a matrix describing the given mapping in terms of homogeneous Cartesian coordinates.

Full work available at URL: https://arxiv.org/abs/1210.1922

zbMATH Keywords

singular valueslinear mappingaxonometry

Mathematics Subject Classification ID

Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Eigenvalues, singular values, and eigenvectors (15A18) Projective analytic geometry (51N15) Descriptive geometry (51N05)

Related Items (6)

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