Timeline for Examples of common false beliefs in mathematics
Current License: CC BY-SA 2.5
5 events
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| Jan 28, 2011 at 21:24 | comment | added | Mark Meckes | Of course it's not bilinear -- an "inner product" on a complex vector space is defined to be sesquilinear, not bilinear -- I've spent a lot of time trying to get my linear algebra students to remember that. The failure of such a form to generalize to other fields is indeed sad, but I think the richness of Hilbert space theory helps to make up for that disappointment. :) | |
| Jan 28, 2011 at 17:51 | comment | added | David E Speyer |
But that's not a bilinear form. And it has no generalization to other fields (what is it on $\overline{\mathbb{F}_p}$?). How can it be standard? :) I certainly agree that people should know that matrices which are self-adjoint with respect to the standard sesquilinear form are diagonalizable.
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| Jan 28, 2011 at 16:46 | comment | added | Mark Meckes | You seem to have a different definition of "the standard inner product on $\mathbb{C}^n$" than I do. I think that phrase normally refers to the familiar positive definite sesquilinear form, with respect to which self-adjoint matrices are indeed diagonalizable. | |
| Jan 28, 2011 at 16:36 | history | edited | David E Speyer | CC BY-SA 2.5 |
added 3 characters in body
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| Jan 28, 2011 at 16:28 | history | answered | David E Speyer | CC BY-SA 2.5 |