Image:Gram–Schmidt process.svg

[edit] Summary

Steps in Gram–Schmidt process.

[edit] Licensing

I, the copyright holder of this work, hereby release it into the public domain. This applies worldwide. In case this is not legally possible: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law. Afrikaans | Alemannisch | Aragonés | العربية | Asturianu | Български | Català | Česky | Cymraeg | Dansk | Deutsch | Eʋegbe | Ελληνικά | English | Español | Esperanto | Euskara | Estremeñu | فارسی | Français | Galego | 한국어 | हिन्दी | Hrvatski | Ido | Bahasa Indonesia | Íslenska | Italiano | עברית | Kurdî / كوردی | Latina | Lietuvių | Latviešu | Magyar | Македонски | Bahasa Melayu | Nederlands | ‪Norsk (bokmål)‬ | ‪Norsk (nynorsk)‬ | 日本語 | Polski | Português | Ripoarisch | Română | Русский | Shqip | Slovenčina | Slovenščina | Српски / Srpski | Svenska | ไทย | Tagalog | Türkçe | Українська | Tiếng Việt | Walon | ‪中文(简体)‬ | ‪中文(繁體)‬ | zh-yue-hant | +/-

[edit] Source

Created by Gustavb using PSTricks.

[edit] Gram–Schmidt process.tex (PSTricks source)

\TeXtoEPS

\psset{linecolor=black,linewidth=1pt,arrowsize=8pt}
\psset{unit=2cm,linewidth=.8pt}
\pspicture*(-1.1,-.2)(3.6,2.2)

\psline{->}(0,0)(3,1)                      % u1
\psline{->}(0,0)(2,2)                      % v2
\psline{->}(0,0)(2.4,.8)                   % proj u1 v2
\psline{->}(0,0)(-.4,1.2)                  % u2
\psline{->}(0,0)(.9486832980,.3162277660)  % e1
\psline{->}(0,0)(-.3162277660,.9486832980) % e2

\psset{linestyle=dashed,dashadjust=false,linewidth=.5pt}
\psline[dash=.12 .1](2,2)(2.4,.8)
\psline[dash=.12 .1](2,2)(-.4,1.2)

\uput{6pt}[315](3,1){\psscalebox{1.6}{${\bf u}_1$}}
\uput{4pt}[25](3,1){\psscalebox{1.6}{${\bf v}_1$}}
\uput{6pt}[335](2,2){\psscalebox{1.6}{${\bf v}_2$}}
\uput{12pt}[265](2.4,.8){\psscalebox{1.2}{${\rm proj}_{{\bf u}_1}{\bf v}_2$}}
\uput{6pt}[200](-.4,1.2){\psscalebox{1.6}{${\bf u}_2$}}

\uput{10pt}[270](.9486832980,.3162277660){\psscalebox{1.6}{${\bf e}_1$}}
\uput{6pt}[220](-.3162277660,.9486832980){\psscalebox{1.6}{${\bf e}_2$}}

\endpspicture

\endTeXtoEPS
\nopagenumbers
\end

[edit] Instructions

1. Create EPS
   

   $ tex Gram-Schmidt_process.tex && dvips -E Gram-Schmidt_process.dvi
   

2. Outline fonts
   

   $ eps2eps -dNOCACHE Gram-Schmidt_process.ps Gram-Schmidt_process2.eps
   

3. Fix bounding box
   

   $ ps2epsi Gram-Schmidt_process2.eps Gram-Schmidt_process.eps
   

4. Convert to Sketch
   

   $ pstoedit -f sk Gram-Schmidt_process.eps Gram-Schmidt_process.sk
   

5. Convert to SVG
   

   $ skconvert Gram-Schmidt_process.sk Gram-Schmidt_process.svg
   

6. Fix Gram-Schmidt_process.svg with Inkscape

• Gram–Schmidt process
• Talk:Gram–Schmidt process
• User:Gustavb/Gallery