Timeline for What is the difference between matrix theory and linear algebra?
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11 events
| when toggle format | what | by | license | comment | |
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| Jun 10, 2010 at 8:45 | comment | added | Harry Gindi | Of course Dieudonne meant "elementary" as in "simple and foundational", here not using "simple" to mean easy, but simple in the sense of structural complexity. It's not an arrogant statement about how easy he thinks linear algebra is, but rather a castigation of those "generations of professors and textbook writers" who turned an elegant subject into a jumbled mess. | |
| Apr 4, 2010 at 21:26 | comment | added | Yemon Choi | Jon: No, I would guess that the "and its applications" line takes care of that. I just don't think having a pop at Dieudonné is particularly justified; context would suggest he had something different in mind from what you do. (For the record, I dislike dividing mathematics into supposedly disjoint areas, but sometimes a vague demarcation is useful. The overlap between linear algebra and analysis is indeed full of unfathomed depths, as you say.) | |
| Apr 4, 2010 at 20:18 | comment | added | Jon | Yemon, do you think the Journal of Linear Algebra and its applcations should be renamed? | |
| Apr 4, 2010 at 19:25 | comment | added | Yemon Choi | It should also be pointed out that the "analytic parts of linear algebra" are more properly thought of as linear analysis, or in the case of operator monotone functions and calculations with the c.b. norm, even as non-linear analysis. I think castigating Dieudonné for this quote is taking unnecessary umbrage. | |
| Apr 4, 2010 at 18:53 | comment | added | Tile | I don't think that there are many who can claim to have a better understanding of that things than Dieudonné. So instead of trying so hard to misunderstand him, try to find a meaning in his comment. | |
| Apr 4, 2010 at 18:06 | comment | added | Jon | It is ironic that a textbook on analysis would make such an outrageous claim on the trivially of another field: the analytic parts of linear algebra are truly deep and quite actively researched. See, for example, Loewner's classification of matrix-monotone functions, or most any paper in quantum Shannon theory. Additionally, the entire field of quantum information theory (QIT) is essentially the study of unitary and self-adjoint operators on tensor products of Hilbert spaces, and a large majority the interesting questions in QIT retain 99% of their interest in the finite-dimensional case. | |
| Mar 31, 2010 at 9:04 | comment | added | Martin Brandenburg | I love this quote! Ok, the authors appear arrogant at many times, but they are right ;). | |
| Mar 30, 2010 at 22:50 | comment | added | Konrad Waldorf | I also added a similar statement of Dieudonné about the Riemann integral. | |
| Mar 30, 2010 at 22:35 | comment | added | Konrad Waldorf | Done. :-) | |
| Mar 30, 2010 at 22:30 | comment | added | Harry Gindi | You should add this to the great quotes in mathematics thread. | |
| Mar 30, 2010 at 22:06 | history | answered | Konrad Waldorf | CC BY-SA 2.5 |