| Title:
|
On the matrices of central linear mappings (English) |
| Author:
|
Havlicek, Hans |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
121 |
| Issue:
|
2 |
| Year:
|
1996 |
| Pages:
|
151-156 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
linear mapping |
| Keyword:
|
axonometry |
| Keyword:
|
singular values |
| MSC:
|
15A18 |
| MSC:
|
51N05 |
| MSC:
|
51N15 |
| MSC:
|
51N20 |
| MSC:
|
68U05 |
| idZBL:
|
Zbl 0863.51020 |
| idMR:
|
MR1400607 |
| DOI:
|
10.21136/MB.1996.126103 |
| . |
| Date available:
|
2009-09-24T21:17:39Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126103 |
| . |
| Reference:
|
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| Reference:
|
[2] Brauner H.: Lineare Abbildungen aus euklidischen Räumen.Beitr. Algebra u. Geometrie 21 (1986), 5-26. Zbl 0589.51004, MR 0839966 |
| Reference:
|
[3] Brauner H.: Zum Satz von Pohlke in n-dimensionalen euklidischen Räumen.Sitzungsber. österreich. Akad. Wiss., Math.-Natur. Kl. 195 (1986), 585-591. MR 0894185 |
| Reference:
|
[4] Havel V.: On decomposition of singular mappings.(In Czech). Časopis Pěst. Mat. 85 (1960), 439-446. MR 0126456 |
| Reference:
|
[5] Paukowitsch P.: Fundamental ideas for computer-supported descriptive geometry.Comput. & Graphics 12 (1988), 3-14. 10.1016/0097-8493(88)90003-9 |
| Reference:
|
[6] Szabó J.: Eine analytische Bedingung dafür, daß eine Zentralaxonometrie Zentralprojektion ist.Publ. Math. Debrecen 44 (1994), 381-390. MR 1291984 |
| Reference:
|
[7] Szabó J., Stachel H., Vogel H.: Ein Satz über die Zentralaxonometrie.Sitzungsber. österreich. Akad. Wiss., Math.-Natur. Kl. 203 (1994), 1-11. MR 1335603 |
| Reference:
|
[8] Strang G.: Linear Algebra and Its Applications.Зrd ed. Harcourt Brace Jovanovich, San Diego, 1988. MR 0575349 |
| . |
