The usual way to represent an Affine Transform is by using a
System Message: WARNING/2 (2 \times 3)
latex exited with error:
[stderr]
[stdout]
This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian)
entering extended mode
(./math.tex
LaTeX2e <2009/09/24>
Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh
yphenation, loaded.
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(/usr/share/texmf-texlive/tex/latex/amsmath/amsmath.sty
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(/usr/share/texmf-texlive/tex/latex/amsmath/amstext.sty
(/usr/share/texmf-texlive/tex/latex/amsmath/amsgen.sty))
(/usr/share/texmf-texlive/tex/latex/amsmath/amsbsy.sty)
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(/usr/share/texmf-texlive/tex/latex/amscls/amsthm.sty)
(/usr/share/texmf-texlive/tex/latex/amsfonts/amssymb.sty
(/usr/share/texmf-texlive/tex/latex/amsfonts/amsfonts.sty))
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Package: `euler’ v2.5 <1995/03/05> (FJ and FMi)
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(/usr/share/texmf-texlive/tex/latex/graphics/dvips.def)
(/usr/share/texmf-texlive/tex/latex/graphics/dvipsnam.def))
! LaTeX Error: File `bbm.sty’ not found.
Type X to quit or <RETURN> to proceed,
or enter new name. (Default extension: sty)
Enter file name:
! Emergency stop.
<read *>
l.11 ...ackage{amsmath}\usepackage{bbm}\usepackage
{colortbl}^^M
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matrix.
System Message: WARNING/2 ( A = \begin{bmatrix}
a_{00} & a_{01} \\
a_{10} & a_{11}
\end{bmatrix}_{2 \times 2}
B = \begin{bmatrix}
b_{00} \\
b_{10}
\end{bmatrix}_{2 \times 1}
M = \begin{bmatrix}
A & B
\end{bmatrix}
=
\begin{bmatrix}
a_{00} & a_{01} & b_{00} \\
a_{10} & a_{11} & b_{10}
\end{bmatrix}_{2 \times 3})
latex exited with error:
[stderr]
[stdout]
This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian)
entering extended mode
(./math.tex
LaTeX2e <2009/09/24>
Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh
yphenation, loaded.
(/usr/share/texmf-texlive/tex/latex/base/article.cls
Document Class: article 2007/10/19 v1.4h Standard LaTeX document class
(/usr/share/texmf-texlive/tex/latex/base/size12.clo))
(/usr/share/texmf-texlive/tex/latex/base/inputenc.sty
(/usr/share/texmf-texlive/tex/latex/ucs/utf8x.def))
(/usr/share/texmf-texlive/tex/latex/ucs/ucs.sty
(/usr/share/texmf-texlive/tex/latex/ucs/data/uni-global.def))
(/usr/share/texmf-texlive/tex/latex/amsmath/amsmath.sty
For additional information on amsmath, use the `?’ option.
(/usr/share/texmf-texlive/tex/latex/amsmath/amstext.sty
(/usr/share/texmf-texlive/tex/latex/amsmath/amsgen.sty))
(/usr/share/texmf-texlive/tex/latex/amsmath/amsbsy.sty)
(/usr/share/texmf-texlive/tex/latex/amsmath/amsopn.sty))
(/usr/share/texmf-texlive/tex/latex/amscls/amsthm.sty)
(/usr/share/texmf-texlive/tex/latex/amsfonts/amssymb.sty
(/usr/share/texmf-texlive/tex/latex/amsfonts/amsfonts.sty))
(/usr/share/texmf-texlive/tex/latex/tools/bm.sty)
(/usr/share/texmf-texlive/tex/latex/euler/euler.sty
Package: `euler’ v2.5 <1995/03/05> (FJ and FMi)
) (/usr/share/texmf-texlive/tex/latex/graphics/color.sty
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(/usr/share/texmf-texlive/tex/latex/graphics/dvips.def)
(/usr/share/texmf-texlive/tex/latex/graphics/dvipsnam.def))
! LaTeX Error: File `bbm.sty’ not found.
Type X to quit or <RETURN> to proceed,
or enter new name. (Default extension: sty)
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<read *>
l.11 ...ackage{amsmath}\usepackage{bbm}\usepackage
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Considering that we want to transform a 2D vector
System Message: WARNING/2 (X = \begin{bmatrix}x \\ y\end{bmatrix})
latex exited with error:
[stderr]
[stdout]
This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian)
entering extended mode
(./math.tex
LaTeX2e <2009/09/24>
Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh
yphenation, loaded.
(/usr/share/texmf-texlive/tex/latex/base/article.cls
Document Class: article 2007/10/19 v1.4h Standard LaTeX document class
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(/usr/share/texmf-texlive/tex/latex/base/inputenc.sty
(/usr/share/texmf-texlive/tex/latex/ucs/utf8x.def))
(/usr/share/texmf-texlive/tex/latex/ucs/ucs.sty
(/usr/share/texmf-texlive/tex/latex/ucs/data/uni-global.def))
(/usr/share/texmf-texlive/tex/latex/amsmath/amsmath.sty
For additional information on amsmath, use the `?’ option.
(/usr/share/texmf-texlive/tex/latex/amsmath/amstext.sty
(/usr/share/texmf-texlive/tex/latex/amsmath/amsgen.sty))
(/usr/share/texmf-texlive/tex/latex/amsmath/amsbsy.sty)
(/usr/share/texmf-texlive/tex/latex/amsmath/amsopn.sty))
(/usr/share/texmf-texlive/tex/latex/amscls/amsthm.sty)
(/usr/share/texmf-texlive/tex/latex/amsfonts/amssymb.sty
(/usr/share/texmf-texlive/tex/latex/amsfonts/amsfonts.sty))
(/usr/share/texmf-texlive/tex/latex/tools/bm.sty)
(/usr/share/texmf-texlive/tex/latex/euler/euler.sty
Package: `euler’ v2.5 <1995/03/05> (FJ and FMi)
) (/usr/share/texmf-texlive/tex/latex/graphics/color.sty
(/etc/texmf/tex/latex/config/color.cfg)
(/usr/share/texmf-texlive/tex/latex/graphics/dvips.def)
(/usr/share/texmf-texlive/tex/latex/graphics/dvipsnam.def))
! LaTeX Error: File `bbm.sty’ not found.
Type X to quit or <RETURN> to proceed,
or enter new name. (Default extension: sty)
Enter file name:
! Emergency stop.
<read *>
l.11 ...ackage{amsmath}\usepackage{bbm}\usepackage
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by using
System Message: WARNING/2 (A)
latex exited with error:
[stderr]
[stdout]
This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian)
entering extended mode
(./math.tex
LaTeX2e <2009/09/24>
Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh
yphenation, loaded.
(/usr/share/texmf-texlive/tex/latex/base/article.cls
Document Class: article 2007/10/19 v1.4h Standard LaTeX document class
(/usr/share/texmf-texlive/tex/latex/base/size12.clo))
(/usr/share/texmf-texlive/tex/latex/base/inputenc.sty
(/usr/share/texmf-texlive/tex/latex/ucs/utf8x.def))
(/usr/share/texmf-texlive/tex/latex/ucs/ucs.sty
(/usr/share/texmf-texlive/tex/latex/ucs/data/uni-global.def))
(/usr/share/texmf-texlive/tex/latex/amsmath/amsmath.sty
For additional information on amsmath, use the `?’ option.
(/usr/share/texmf-texlive/tex/latex/amsmath/amstext.sty
(/usr/share/texmf-texlive/tex/latex/amsmath/amsgen.sty))
(/usr/share/texmf-texlive/tex/latex/amsmath/amsbsy.sty)
(/usr/share/texmf-texlive/tex/latex/amsmath/amsopn.sty))
(/usr/share/texmf-texlive/tex/latex/amscls/amsthm.sty)
(/usr/share/texmf-texlive/tex/latex/amsfonts/amssymb.sty
(/usr/share/texmf-texlive/tex/latex/amsfonts/amsfonts.sty))
(/usr/share/texmf-texlive/tex/latex/tools/bm.sty)
(/usr/share/texmf-texlive/tex/latex/euler/euler.sty
Package: `euler’ v2.5 <1995/03/05> (FJ and FMi)
) (/usr/share/texmf-texlive/tex/latex/graphics/color.sty
(/etc/texmf/tex/latex/config/color.cfg)
(/usr/share/texmf-texlive/tex/latex/graphics/dvips.def)
(/usr/share/texmf-texlive/tex/latex/graphics/dvipsnam.def))
! LaTeX Error: File `bbm.sty’ not found.
Type X to quit or <RETURN> to proceed,
or enter new name. (Default extension: sty)
Enter file name:
! Emergency stop.
<read *>
l.11 ...ackage{amsmath}\usepackage{bbm}\usepackage
{colortbl}^^M
No pages of output.
Transcript written on math.log.
and
System Message: WARNING/2 (B)
latex exited with error:
[stderr]
[stdout]
This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian)
entering extended mode
(./math.tex
LaTeX2e <2009/09/24>
Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh
yphenation, loaded.
(/usr/share/texmf-texlive/tex/latex/base/article.cls
Document Class: article 2007/10/19 v1.4h Standard LaTeX document class
(/usr/share/texmf-texlive/tex/latex/base/size12.clo))
(/usr/share/texmf-texlive/tex/latex/base/inputenc.sty
(/usr/share/texmf-texlive/tex/latex/ucs/utf8x.def))
(/usr/share/texmf-texlive/tex/latex/ucs/ucs.sty
(/usr/share/texmf-texlive/tex/latex/ucs/data/uni-global.def))
(/usr/share/texmf-texlive/tex/latex/amsmath/amsmath.sty
For additional information on amsmath, use the `?’ option.
(/usr/share/texmf-texlive/tex/latex/amsmath/amstext.sty
(/usr/share/texmf-texlive/tex/latex/amsmath/amsgen.sty))
(/usr/share/texmf-texlive/tex/latex/amsmath/amsbsy.sty)
(/usr/share/texmf-texlive/tex/latex/amsmath/amsopn.sty))
(/usr/share/texmf-texlive/tex/latex/amscls/amsthm.sty)
(/usr/share/texmf-texlive/tex/latex/amsfonts/amssymb.sty
(/usr/share/texmf-texlive/tex/latex/amsfonts/amsfonts.sty))
(/usr/share/texmf-texlive/tex/latex/tools/bm.sty)
(/usr/share/texmf-texlive/tex/latex/euler/euler.sty
Package: `euler’ v2.5 <1995/03/05> (FJ and FMi)
) (/usr/share/texmf-texlive/tex/latex/graphics/color.sty
(/etc/texmf/tex/latex/config/color.cfg)
(/usr/share/texmf-texlive/tex/latex/graphics/dvips.def)
(/usr/share/texmf-texlive/tex/latex/graphics/dvipsnam.def))
! LaTeX Error: File `bbm.sty’ not found.
Type X to quit or <RETURN> to proceed,
or enter new name. (Default extension: sty)
Enter file name:
! Emergency stop.
<read *>
l.11 ...ackage{amsmath}\usepackage{bbm}\usepackage
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No pages of output.
Transcript written on math.log.
, we can do it equivalently with:
System Message: WARNING/2 (T = A \cdot \begin{bmatrix}x \\ y\end{bmatrix} + B)
latex exited with error:
[stderr]
[stdout]
This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian)
entering extended mode
(./math.tex
LaTeX2e <2009/09/24>
Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh
yphenation, loaded.
(/usr/share/texmf-texlive/tex/latex/base/article.cls
Document Class: article 2007/10/19 v1.4h Standard LaTeX document class
(/usr/share/texmf-texlive/tex/latex/base/size12.clo))
(/usr/share/texmf-texlive/tex/latex/base/inputenc.sty
(/usr/share/texmf-texlive/tex/latex/ucs/utf8x.def))
(/usr/share/texmf-texlive/tex/latex/ucs/ucs.sty
(/usr/share/texmf-texlive/tex/latex/ucs/data/uni-global.def))
(/usr/share/texmf-texlive/tex/latex/amsmath/amsmath.sty
For additional information on amsmath, use the `?’ option.
(/usr/share/texmf-texlive/tex/latex/amsmath/amstext.sty
(/usr/share/texmf-texlive/tex/latex/amsmath/amsgen.sty))
(/usr/share/texmf-texlive/tex/latex/amsmath/amsbsy.sty)
(/usr/share/texmf-texlive/tex/latex/amsmath/amsopn.sty))
(/usr/share/texmf-texlive/tex/latex/amscls/amsthm.sty)
(/usr/share/texmf-texlive/tex/latex/amsfonts/amssymb.sty
(/usr/share/texmf-texlive/tex/latex/amsfonts/amsfonts.sty))
(/usr/share/texmf-texlive/tex/latex/tools/bm.sty)
(/usr/share/texmf-texlive/tex/latex/euler/euler.sty
Package: `euler’ v2.5 <1995/03/05> (FJ and FMi)
) (/usr/share/texmf-texlive/tex/latex/graphics/color.sty
(/etc/texmf/tex/latex/config/color.cfg)
(/usr/share/texmf-texlive/tex/latex/graphics/dvips.def)
(/usr/share/texmf-texlive/tex/latex/graphics/dvipsnam.def))
! LaTeX Error: File `bbm.sty’ not found.
Type X to quit or <RETURN> to proceed,
or enter new name. (Default extension: sty)
Enter file name:
! Emergency stop.
<read *>
l.11 ...ackage{amsmath}\usepackage{bbm}\usepackage
{colortbl}^^M
No pages of output.
Transcript written on math.log.
or
System Message: WARNING/2 (T = M \cdot [x, y, 1]^{T})
latex exited with error:
[stderr]
[stdout]
This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian)
entering extended mode
(./math.tex
LaTeX2e <2009/09/24>
Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh
yphenation, loaded.
(/usr/share/texmf-texlive/tex/latex/base/article.cls
Document Class: article 2007/10/19 v1.4h Standard LaTeX document class
(/usr/share/texmf-texlive/tex/latex/base/size12.clo))
(/usr/share/texmf-texlive/tex/latex/base/inputenc.sty
(/usr/share/texmf-texlive/tex/latex/ucs/utf8x.def))
(/usr/share/texmf-texlive/tex/latex/ucs/ucs.sty
(/usr/share/texmf-texlive/tex/latex/ucs/data/uni-global.def))
(/usr/share/texmf-texlive/tex/latex/amsmath/amsmath.sty
For additional information on amsmath, use the `?’ option.
(/usr/share/texmf-texlive/tex/latex/amsmath/amstext.sty
(/usr/share/texmf-texlive/tex/latex/amsmath/amsgen.sty))
(/usr/share/texmf-texlive/tex/latex/amsmath/amsbsy.sty)
(/usr/share/texmf-texlive/tex/latex/amsmath/amsopn.sty))
(/usr/share/texmf-texlive/tex/latex/amscls/amsthm.sty)
(/usr/share/texmf-texlive/tex/latex/amsfonts/amssymb.sty
(/usr/share/texmf-texlive/tex/latex/amsfonts/amsfonts.sty))
(/usr/share/texmf-texlive/tex/latex/tools/bm.sty)
(/usr/share/texmf-texlive/tex/latex/euler/euler.sty
Package: `euler’ v2.5 <1995/03/05> (FJ and FMi)
) (/usr/share/texmf-texlive/tex/latex/graphics/color.sty
(/etc/texmf/tex/latex/config/color.cfg)
(/usr/share/texmf-texlive/tex/latex/graphics/dvips.def)
(/usr/share/texmf-texlive/tex/latex/graphics/dvipsnam.def))
! LaTeX Error: File `bbm.sty’ not found.
Type X to quit or <RETURN> to proceed,
or enter new name. (Default extension: sty)
Enter file name:
! Emergency stop.
<read *>
l.11 ...ackage{amsmath}\usepackage{bbm}\usepackage
{colortbl}^^M
No pages of output.
Transcript written on math.log.
System Message: WARNING/2 (T = \begin{bmatrix}
a_{00}x + a_{01}y + b_{00} \\
a_{10}x + a_{11}y + b_{10}
\end{bmatrix})
latex exited with error:
[stderr]
[stdout]
This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian)
entering extended mode
(./math.tex
LaTeX2e <2009/09/24>
Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh
yphenation, loaded.
(/usr/share/texmf-texlive/tex/latex/base/article.cls
Document Class: article 2007/10/19 v1.4h Standard LaTeX document class
(/usr/share/texmf-texlive/tex/latex/base/size12.clo))
(/usr/share/texmf-texlive/tex/latex/base/inputenc.sty
(/usr/share/texmf-texlive/tex/latex/ucs/utf8x.def))
(/usr/share/texmf-texlive/tex/latex/ucs/ucs.sty
(/usr/share/texmf-texlive/tex/latex/ucs/data/uni-global.def))
(/usr/share/texmf-texlive/tex/latex/amsmath/amsmath.sty
For additional information on amsmath, use the `?’ option.
(/usr/share/texmf-texlive/tex/latex/amsmath/amstext.sty
(/usr/share/texmf-texlive/tex/latex/amsmath/amsgen.sty))
(/usr/share/texmf-texlive/tex/latex/amsmath/amsbsy.sty)
(/usr/share/texmf-texlive/tex/latex/amsmath/amsopn.sty))
(/usr/share/texmf-texlive/tex/latex/amscls/amsthm.sty)
(/usr/share/texmf-texlive/tex/latex/amsfonts/amssymb.sty
(/usr/share/texmf-texlive/tex/latex/amsfonts/amsfonts.sty))
(/usr/share/texmf-texlive/tex/latex/tools/bm.sty)
(/usr/share/texmf-texlive/tex/latex/euler/euler.sty
Package: `euler’ v2.5 <1995/03/05> (FJ and FMi)
) (/usr/share/texmf-texlive/tex/latex/graphics/color.sty
(/etc/texmf/tex/latex/config/color.cfg)
(/usr/share/texmf-texlive/tex/latex/graphics/dvips.def)
(/usr/share/texmf-texlive/tex/latex/graphics/dvipsnam.def))
! LaTeX Error: File `bbm.sty’ not found.
Type X to quit or <RETURN> to proceed,
or enter new name. (Default extension: sty)
Enter file name:
! Emergency stop.
<read *>
l.11 ...ackage{amsmath}\usepackage{bbm}\usepackage
{colortbl}^^M
No pages of output.
Transcript written on math.log.