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Are pivots a core concept? Good question. They don't feel that way to me. They seem more like the implementation detail of an algorithm (Gaussian elimination).
by gruseom 15y ago
Are pivots a core concept?
Good question. They don't feel that way to me. They seem more like the implementation detail of an algorithm (Gaussian elimination). Is the algorithm itself a core concept? Hard to say no to that, I guess, but I wonder.
What about what Strang calls the "row picture" vs. the "column picture"? There you have two fundamentally different geometric interpretations of linear equations. That was a revelation to me. When I studied linear algebra a long time ago, I don't remember encountering the column interpretation. Perhaps I did and didn't pay attention; I was more interested in symbolic manipulation at the time, whereas now I want a sense of what the symbols mean geometrically.
- tptacek 15y agoThe intro lecture on row/column pictures made this click for me better than the book did: http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/video-lectures/lecture-1-the-geometry-of-linear-equations http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-... 22:00 in.
- mechanical_fish 15y agoAmusingly, I'm in the entirely opposite boat. I managed to get an entire Ph.D. in solid state physics without taking an actual course in linear algebra (a procedure that I do not recommend, but everyone is young and foolish once). So I've got some idea of what vector spaces are about geometrically -- otherwise, graduate quantum mechanics would have been impossible to navigate -- but I'm really bad at manipulating the actual symbols. And, incidentally, I'm planning to attempt most of the problems. I've cherry-picked my way through this subject before, and I was ultimately displeased with the results. They say that the problem with an autodidact is that he has a fool for a teacher, and with linear algebra I learned that the hard way. Fortunately, now they've invented Open Courseware, Amazon.com, and HN, so I'll give the fool another chance.
- gruseom 15y agoI propose that we explicitly mention any exercises that we stumble over. Yeah it may make us look like idiots but we're destined to look like idiots anyway, and there's a major upside: we're going to stumble over different things, which means we can provide good explanations to one another, and learn better. I have a few examples of this sitting at home but am hacking at the library at the moment. It is heavenly quiet here. I will post them later.
- akkartik 15y agoKinda half-baked aside: Sometimes I think it would be incredibly valuable to share our intermediate steps when working out solutions to problems. Kinda like how it's fascinating to see PG write that essay.
- mechanical_fish 15y agoSo far I'm stumbling over the part where I actually sit down and read the book and do the problems. ;) But my book only arrived last week, so I'm not feeling too guilty yet.
- gruseom 15y agoOne function of this group is to turn guilt into shame. :)