Matrix Transpose
Charles B. Cameron
symbol. Can anyone recommend a standard symbol for the superscript?
Candidates which occur to me are T, \top, and \intercal.
Charles B. Cameron
John Harper
$A^T$ makes T italic which may not suit you. In my 'umble opinion
$A^{\top}$ makes T too thin,
$A^{\intercal}$ puts T too low,
$A^{\sffamily T}$ doesn't work: \sffamily is invalid in math mode,
$A^{\mbox{\sffamily T}}$ makes T too big,
$A^{\textsf{T}}$ makes T too big, but
$A^{\sf T}$ is just right.
Curiously, Lamport's LaTeX2e book does not mention \sf (which was the
usual LaTeX 2.09 method for getting sanserif) though p228 does mention
\tt, \sc and \sl, saying they still work but shouldn't be used.
I seem to have found a case where that advice is unhelpful.
Lamport also says on p226 that \textsf cannot be used in math mode.
It caused no error message for me.
John Harper, School of Mathematical and Computing Sciences,
Victoria University, PO Box 600, Wellington, New Zealand
e-mail john....@vuw.ac.nz phone (+64)(4)463 5341 fax (+64)(4)463 5045
jim green
> Candidates which occur to me are T, \top, and \intercal.
Usually T, but I have seen t and * used (in a real setting).
You might like to try a roman T (\mathrm{T}) since is really
a text abbreviation rather than a variable. Some people think
this is over-fussy or formulaic. I think its prettier.
Jim
--
J. J. Green, Department of Applied Mathematics, Hicks Bd.,
Hounsfield Rd., University of Sheffield, Sheffield, UK.
+44 (0114) 222 3742, http://www.vindaloo.uklinux.net/jjg
Walter Schmidt
>
> The classics (Birkhoff & Mac Lane, Aitken) used ' but if you want T,
> $A^T$ makes T italic which may not suit you. In my 'umble opinion
> $A^{\top}$ makes T too thin,
> $A^{\intercal}$ puts T too low,
> $A^{\sffamily T}$ doesn't work: \sffamily is invalid in math mode,
> $A^{\mbox{\sffamily T}}$ makes T too big,
> $A^{\textsf{T}}$ makes T too big, but
>
> $A^{\sf T}$ is just right.
>
> Curiously, Lamport's LaTeX2e book does not mention \sf
Lamport _does_ mention \mathsf, and that's the right
way to do it:
$A^{\mathsf{T}}$
best wishes
Walter
Charles B. Cameron
> I would like to express the transpose of a matrix using a superscript
> symbol. Can anyone recommend a standard symbol for the superscript?
[...]
Thanks to all who answered. Many different answers were considered and
described to me in detail. What a great newsgroup this is! I don't
know anywhere else where there is so much knowledge about how
mathematics should look in print.
Charles B. Cameron
Giuseppe Bilotta
> Hi Charles
>
> > Candidates which occur to me are T, \top, and \intercal.
>
> Usually T, but I have seen t and * used (in a real setting).
> You might like to try a roman T (\mathrm{T}) since is really
> a text abbreviation rather than a variable. Some people think
> this is over-fussy or formulaic. I think its prettier.
Of course then there's the problem of *where* to put it ... it should
get on the *left* of the A, not on its right (at least that's the way
I was taught)
--
Giuseppe "Oblomov" Bilotta
Can't you see
It all makes perfect sense
Expressed in dollar and cents
Pounds shillings and pence
(Roger Waters)
Einar S. Idsø
Giuseppe Bilotta <bilo...@hotpop.com> wrote:
> > Usually T, but I have seen t and * used (in a real setting).
> > You might like to try a roman T (\mathrm{T}) since is really
> > a text abbreviation rather than a variable. Some people think
> > this is over-fussy or formulaic. I think its prettier.
> Of course then there's the problem of *where* to put it ... it should
> get on the *left* of the A, not on its right (at least that's the way
> I was taught)
You have _got_ to be kidding! In all my textbooks on mathematics,
systems theory and control theory, I've never once come across the
transpose sign being on the left.
Which book did you use? Perhaps an arabic book in which text is read
from right to left? ;-)
Einar
Giuseppe Bilotta
LOL. No, that's the way we use it in Italy. But judging from your
name and email address you wouldn't have come across many Italian
textbooks :)
Scott Pakin
> In article <3EF8B01A...@aplcenMP.apl.jhu.edu>,
> Charles B. Cameron <came...@aplcenMP.apl.jhu.edu> wrote:
>
>>I would like to express the transpose of a matrix using a superscript
>>symbol. Can anyone recommend a standard symbol for the superscript?
>>
>>Candidates which occur to me are T, \top, and \intercal.
.
.
> $A^{\sffamily T}$ doesn't work: \sffamily is invalid in math mode,
Try $A^{\mathsf{T}}$ instead.
> $A^{\mbox{\sffamily T}}$ makes T too big,
amstext provides a math-mode replacement for \mbox called \text
that's smart about script style. You can try, for example,
$A^{\text{\tiny\sffamily T}}$.
-- Scott
Lars Madsen
> LOL. No, that's the way we use it in Italy. But judging from your
> name and email address you wouldn't have come across many Italian
> textbooks :)
>
I've found it in english books as well. This is why it is always agood
idea to explain your syntax a little.
/daleif
Art Werschulz
Walter Schmidt <wsc...@arcor.de> writes:
> John Harper schrieb:
> >
> > $A^{\sf T}$ is just right.
>
> Lamport _does_ mention \mathsf, and that's the right
> way to do it:
> $A^{\mathsf{T}}$
One could also use
$A^{\mathrm{T}}$
to produce a roman "T". Why would sans-serif be preferable to roman
for producing the transpose symbol? Since the "T" is an abbreviation,
it seems to me that it's playing the same role as "sin", which is
typically done as roman.
--
Art Werschulz (8-{)} "Metaphors be with you." -- bumper sticker
GCS/M (GAT): d? -p+ c++ l u+(-) e--- m* s n+ h f g+ w+ t++ r- y?
Internet: a...@cs.columbia.edu<a href="http://www.cs.columbia.edu/~agw/">WWW</a>
ATTnet: Columbia U. (212) 939-7060, Fordham U. (212) 636-6325
Dan Luecking
>amstext provides a math-mode replacement for \mbox called \text
>that's smart about script style. You can try, for example,
>$A^{\text{\tiny\sffamily T}}$.
It makes no difference how smart it is about script style if you
just override it with \tiny ;-)
I find the \tiny makes it too low. I feel the top of the T should
rise above the top of the A. Still, it looks OK.
A notation I don't recall being mentioned is $A^t$ where the t is
lowercase (in some style) or $A^*$ (which is often used for the
hermitian adjoint, but that is the same as the transpose if the
matrix entries are real). I've also seen $\bar{A}$, $A^{\dag}$ and
${}^{t}\!\!A$.
Dan
--
Dan Luecking Department of Mathematical Sciences
University of Arkansas Fayetteville, Arkansas 72701
luecking at uark dot edu
Michele Dondi
<e...@dont.want.spam.to.itk.ntnu.no> wrote:
>> Of course then there's the problem of *where* to put it ... it should
>> get on the *left* of the A, not on its right (at least that's the way
>> I was taught)
>
>You have _got_ to be kidding! In all my textbooks on mathematics,
>systems theory and control theory, I've never once come across the
>transpose sign being on the left.
Well, I've seen it on the left more than once in both english and
italian textbooks. One setting in which this is useful is differential
geometry, for example dealing with cotangent bundle: the symbol
describing a map can be already loaded with chart index(es), and a
'^{-1}'.
See, for example, the following fragment from some notes by one of my
teachers, that I typeset a few years ago: here, \trn puts reliably a
superscript on the left, thanks to some code gently provided by
Michael J Downes (RIP) on this ng following as an hint a horrible hack
I had previously made to AMS's \sideset...
<EXAMPLE>
La parte significativa
$\ffromto{\phi_\alpha}{\eta_\alpha(U_\alpha)}{\Rd^\ast}$
dell'espressione
locale $\phi_{\alpha\alpha}$ \`e chiamata \emph{configurazione locale}
di
$\phi$ relativamente alla carta $(U_\alpha,\eta_\alpha)$. Chiaramente
\begin{equation}
\phi_\alpha(u)=
\bigl(\trn{\th_{\eta_\alpha^{-1}(u)\alpha}^{-1}}\bigr)(u)
\end{equation}
Le \emph{relazioni di transizione per le $1$-forme} sono, come si
ottiene
facilmente,
\begin{gather}
\label{src2.6b}
\phi_{\alpha'}(u')=
\trn{\bigl(\eta'_{\alpha'\alpha}(u)\bigr)^{-1}}
\phi_\alpha(u)
\\
u'=\eta_{\alpha'}(x), \quad
u=\eta_\alpha(x), \quad
x\in U_\alpha'\cap U_\alpha
\notag
\end{gather}
</EXAMPLE>
Michele
--
>It's because the universe was programmed in C++.
No, no, it was programmed in Forth. See Genesis 1:12:
"And the earth brought Forth ..."
- Robert Israel on sci.math, thread "Why numbers?"
Carl Riehm
On Wed, 25 Jun 2003 12:37:57 +0200, "Einar S. Idsř"
<e...@dont.want.spam.to.itk.ntnu.no> wrote:
>
> >> Of course then there's the problem of *where* to put it ... it should
> >> get on the *left* of the A, not on its right (at least that's the way
> >> I was taught)
> >
> >You have _got_ to be kidding! In all my textbooks on mathematics,
> >systems theory and control theory, I've never once come across the
> >transpose sign being on the left.
Actually in Bourbaki's Algebre Lineare (at least in the first edition),
the transpose symbol "t" is placed on the left. Seems perfectly
reasonable to me, at least if you agree that writing functions as f(x)
rather than (x)f is reasonable (which it isn't of course).
ADH
> news:<3EF8B01A...@aplcenMP.apl.jhu.edu>...
> I would like to express the transpose of a matrix using a superscript
> symbol. Can anyone recommend a standard symbol for the superscript?
>
> Candidates which occur to me are T, \top, and \intercal.
>
perhaps should be mentioned for completeness:) is that however you
decide to typeset the transpose, it's a Very Good Idea to define a
macro (\transpose{A} or whatever) rather than pepper the manuscript
with hardwired notation. In fact, it's a Fairly Bad Idea *not* to
define a macro. One of LaTeX's strengths is its capacity to structure
source files logically, in a way that reflects the ideas conveyed in
the document. Hard-wiring fonts throws away a good part of that
advantage.
On a related note, it's a good idea to define logical aliases for
fonts, as in:
\newcommand{\Map}[1]{\mathcal{#1}}
\newcommand{\Number}[1]{\mathbf{#1}}
\newcommand{\Sheaf}[1]{\mathcal{#1}}
The actual macros used in the manuscript are then defined in terms of
these, e.g.:
\newcommand{\F}[2]{\Map{F}(#1,#2)}
\newcommand{\O}{\Sheaf{O}}
\newcommand{\R}{\Number{R}}
This scheme (which I learned from the AMS LaTeX documentation)
explicitly encourages consistent notation, and makes the document more
flexible and easier to maintain by localizing the font information in
the preamble. (It may also make the document easier for a human to
read if the macros are well-chosen.)
Surely everyone who has posted in this thread is well aware of these
issues, but they bear repeating since many new users follow this
group, and the habits described above are good ones to cultivate from
the very start of one's LaTeX experience.
--Andy
Andrew D. Hwang
Dept of Mathematics and CS
College of the Holy Cross
Worcester, MA, 01610-2395, USA
Michele Dondi
wrote:
>A relevant point no one has articulated in this thread (but which
>perhaps should be mentioned for completeness:) is that however you
>decide to typeset the transpose, it's a Very Good Idea to define a
>macro (\transpose{A} or whatever) rather than pepper the manuscript
>with hardwired notation. In fact, it's a Fairly Bad Idea *not* to
Well, I had, for one! OK, it was hidden somewhere between the lines of
some code I had pasted in my post...