Timeline for Notation for bilinear form $y^t M z$, where $M$ is a matrix and $y,z$ are vectors.
Current License: CC BY-SA 2.5
8 events
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| Nov 21, 2010 at 2:25 | comment | added | Alex B. | Unfortunately, I am not aware of any standard notation for your restricted sums. Maybe, if you call the original bilinear form $B$, then writing $B_E$ or $B|_E$ would be fine, as long as you clearly point it out that this does not in fact denote a bilinear form. | |
| Nov 20, 2010 at 10:44 | comment | added | Louigi Addario-Berry | Thanks Alex. The point of my question is to have a consistent notation for both the former and the latter, do you have a thought about what one might use in this case? | |
| Nov 20, 2010 at 5:01 | comment | added | Alex B. | Note that a real inner product is usually defined to be non-degenerate, i.e. the matrix $M$ has to be non-singular. If that's not always the case in your situation, then the notation $\langle,\rangle_M$ is misleading. And certainly, the notation $\langle,\rangle_{M,E}$ seems misleading to me since these guys are degenerate. For the former, I would prefer "bilinear form $B(y,z)$", but for the latter, even that would be misleading, since it is not bi-linear. | |
| Nov 19, 2010 at 18:05 | comment | added | Louigi Addario-Berry | Also: the boldface I is meant to be the indicator function of the set E. | |
| Nov 19, 2010 at 18:05 | history | edited | Louigi Addario-Berry | CC BY-SA 2.5 |
Changed "inner product" to "bilinear forms" after a comment suggested this.
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| Nov 19, 2010 at 18:03 | comment | added | Louigi Addario-Berry | Thanks for the suggestions, I will modify my question accordingly! Yes in my situation the matrix is in fact symmetric, I will mention this. | |
| Nov 19, 2010 at 17:52 | comment | added | Dick Palais | I think it would be better (more standard) to call these bilinear forms rather than inner products. Also, did you really mean $R^2$? And what is the meaning of the bold-face I? I think that the pointed bracket notation may be misleading since it might make one expect it to be symmetric---or do you mean to restrict the matrix $M$ to be symmetric? | |
| Nov 19, 2010 at 15:29 | history | asked | Louigi Addario-Berry | CC BY-SA 2.5 |