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-s...@creativetrax.com> To: sage-de...@googlegroups.com; sage-edu <sage-edu@googlegroups.com> Sent: Sunday, June 3, 2012 1:20 AM Subject: [sage-edu] Linear Algebra thematic tutorial 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 -- You received this message because you are subscribed to the Google Groups "sage-edu" group. To post to this group, send email to sage-edu@googlegroups.com. To unsubscribe from this group, send email to sage-edu+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sage-edu?hl=en. -- You received this message because you are subscribed to the Google Groups "sage-edu" group. To post to this group, send email to sage-edu@googlegroups.com. To unsubscribe from this group, send email to sage-edu+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sage-edu?hl=en.
