Linear Algebra thematic tutorial

[Jason Grout]

Hi everyone,

Rob (Beezer), Robert (Bradshaw), William, and I have been working on an
introduction for linear algebra for the next edition of CRC's Handbook
of Linear Algebra. The publisher has agreed that a version of the final
article will be licensed CC-by so that we can include it in our official
documentation. We're planning on including it in the thematic tutorial
section.

We are just about finished with this. I've temporarily put up a version
in the *.sagenb.org servers except sagenb.org (for example,
http://demo.sagenb.org/doc/static/thematic_tutorials/linear_algebra.html, or
if you're logged in,
http://demo.sagenb.org/doc/live/thematic_tutorials/linear_algebra.html
for the live version). We are submitting this on Monday. If you have
any comments or corrections, we'd love to hear them.

I still need to finish some of the references, particularly at the end
of the chapter, and I will probably do a bit more consolidating, since
the chapter is still a bit too long. Anyways, have fun reading!

Thanks,

Jason

[David Joyner]

On Sun, Jun 3, 2012 at 2:20 AM, Jason Grout <jason...@creativetrax.com> wrote:
> Hi everyone,
>

...

>
> We are just about finished with this.  I've temporarily put up a version in
> the *.sagenb.org servers except sagenb.org (for example,
> http://demo.sagenb.org/doc/static/thematic_tutorials/linear_algebra.html, or

Wow - this looks great!

> if you're logged in,

...

>
> Thanks,
>
> Jason
>
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[John H Palmieri]

On Saturday, June 2, 2012 11:20:15 PM UTC-7, jason wrote:

Hi everyone,

Rob (Beezer), Robert (Bradshaw), William, and I have been working on an
introduction for linear algebra for the next edition of CRC's Handbook
of Linear Algebra.  The publisher has agreed that a version of the final
article will be licensed CC-by so that we can include it in our official
documentation.  We're planning on including it in the thematic tutorial
section.

We are just about finished with this.  I've temporarily put up a version
in the *.sagenb.org servers except sagenb.org (for example,
http://demo.sagenb.org/doc/static/thematic_tutorials/linear_algebra.html, or
if you're logged in,
http://demo.sagenb.org/doc/live/thematic_tutorials/linear_algebra.html
for the live version).   We are submitting this on Monday.  If you have
any comments or corrections, we'd love to hear them.

As far as I understand it, there are two approaches to linear algebra in Sage: the one you describe, and then "CombinatorialFreeModule". The latter is good for working with the vector space spanned by symbols 'u', 'v', and 'w', for example, or the vector space spanned by all partitions of 35, or all permutations of [1,2,3,4], or all simplices in some simplicial complex, and as such it is good for constructing algebras and modules.

I wish that these two approaches were more unified, or at least there were good ways to convert between the two. I also wish that you had discussed both approaches, not just one.

--
John

[Gerald Smith]

Hi!

have you ever heard of the Geometric Algebra of Dr. david Hestenes?  It provides a  solid geometric founndation to Linear Algebra and makes the subject far more intelligible than the generally purely algebraic approach taken today. since the theoretical underpinnings of Linera algebra are very rich in geometric implications, this makes a huge advantage in understanding the subject. i have read agaain and agin statements by indivuduals, mostly by people in computer science, that they never really understood Linear algebra until they encountered Geometric Algebra. This is certainlyy the case for me too!   The additions to traditional linear Algebra is first of all, the use of the Outer Product along with the Inner Product right from the beginning. This is vital for  understanding such concepts as the Dterminant of a a Mtrix (the scalr value of the outer product of it row vectors or column vectors) and Cramer's Rule (which becomes a very elementary consequence of the preceding definition og determinant). Then, vectors are given a strict geometric definition but multidemensional and mixed dimensional extensions are introduced.  A complete algebra of adding subtracting multiplying and dividing vectors based on the generalized geometric product of vectors is introduced and its implications developed.  University professors have told me reopeatedly that undergraduuate sdtudents generally fail to really comprehend linear Algebra and I believe this is the natural consequence of teaching a richly geometric subject without any geomtry to speak of. Of course students are not going to understand it! They are blinded.  Use of even the most basic elements would do much to remedy this. Sorry for intruding but I find it hard not to put in a good word for geometric algebra when I get the chance.

Regards,

Gerald Smith

---

From: Jason Grout <jason...@creativetrax.com>
To: sage-...@googlegroups.com; sage-edu <sage...@googlegroups.com>
Sent: Sunday, June 3, 2012 1:20 AM
Subject: [sage-edu] Linear Algebra thematic tutorial

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[Jason Grout]

On 6/3/12 12:03 PM, John H Palmieri wrote:
> I wish that these two approaches were more unified, or at least there
> were good ways to convert between the two. I also wish that you had
> discussed both approaches, not just one.

The audience is people that are in matrix-oriented linear algebra.
However, luckily, the combinat people have excellent documentation.

Is there some tutorial somewhere that we can point people to for more
information (or is the reference manual page the best place?)? We can
definitely put a paragraph or two in about the CombinatorialFreeModule
approach, and a link for more information.

Jason

[Jason Grout]

On 6/11/12 12:34 PM, Michele wrote:
> Hi,
> at page 120-7 of the pdf the example of Elementary matrix
> "elementary_matrix(QQ, row1=3, scale=-2)" misses the matrix size.
> Thanks for the beautiful work,

Thanks! I've corrected it in our source.

Jason