On the matrices of central linear mappings

Hans Havlicek

Mathematica Bohemica (1996)

  • Volume: 121, Issue: 2, page 151-156
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Havlicek, Hans. "On the matrices of central linear mappings." Mathematica Bohemica 121.2 (1996): 151-156. <http://eudml.org/doc/247956>.

@article{Havlicek1996,
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 $\ge 2m-n+1$. This matrix is arising, by a simple manipulation, from a matrix describing the given mapping in terms of homogeneous Cartesian coordinates.},
author = {Havlicek, Hans},
journal = {Mathematica Bohemica},
keywords = {linear mapping; axonometry; singular values; linear mapping; axonometry; singular values},
language = {eng},
number = {2},
pages = {151-156},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the matrices of central linear mappings},
url = {http://eudml.org/doc/247956},
volume = {121},
year = {1996},
}

TY - JOUR
AU - Havlicek, Hans
TI - On the matrices of central linear mappings
JO - Mathematica Bohemica
PY - 1996
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 121
IS - 2
SP - 151
EP - 156
AB - 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 $\ge 2m-n+1$. This matrix is arising, by a simple manipulation, from a matrix describing the given mapping in terms of homogeneous Cartesian coordinates.
LA - eng
KW - linear mapping; axonometry; singular values; linear mapping; axonometry; singular values
UR - http://eudml.org/doc/247956
ER -

References

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  6. Szabó J., Eine analytische Bedingung dafür, daß eine Zentralaxonometrie Zentralprojektion ist, Publ. Math. Debrecen 44 (1994), 381-390. (1994) MR1291984
  7. Szabó J., Stachel H., Vogel H., Ein Satz über die Zentralaxonometrie, Sitzungsber. österreich. Akad. Wiss., Math.-Natur. Kl. 203 (1994), 1-11. (1994) MR1335603
  8. Strang G., Linear Algebra and Its Applications, Зrd ed. Harcourt Brace Jovanovich, San Diego, 1988. (1988) MR0575349

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