MATHEMATICA BOHEMICA, Vol. 121, No. 2, pp. 151-156, 1996

On the matrices of central linear mappings

Hans Havlicek

Hans Havlicek, Abteilung fur Lineare Algebra und Geometrie, Technische Universitat, Wiedner Hauptstrasse 8-10, A-1040 Wien, Austria, e-mail:

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.

Keywords: linear mapping, axonometry, singular values

Classification (MSC91): 51N15, 51N05, 15A18, 68U05

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