| Title: | Mathematics at DEC |
| Moderator: | RUSURE::EDP |
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
From: RHEA::DECWRL::""::GAGLIONE" gaglione@nrl1.decnet" "NRL1" 19-DEC-1985 08:55
To: "stan%clt.dec" <stan%clt.dec@decwrl>
Subj: PROBLEMS(MATH)
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Date: 18 Dec 85 21:56:00 EST
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Reply-To: "NRL1::GAGLIONE" <gaglione@nrl1.decnet>
STAN,
I just saw a copy of the most recent Putnam exam. There is a very
nice algebra problem on it that I would like to share with you:
Let G be a finite group of real matrices(under matrix mult-
iplication). Suppose that the sum of the traces of all the
matrices in G is 0. Prove that the sum of all the matrices
is 0 i.e.,the zero matrix.
| T.R | Title | User | Personal Name | Date | Lines |
|---|---|---|---|---|---|
| 413.1 | Does this help? | ZFC::DERAMO | Frustrated personal name composer | Mon Dec 21 1987 22:26 | 10 |
>> Let G be a finite group of real matrices(under matrix mult-
>> iplication). Suppose that the sum of the traces of all the
>> matrices in G is 0. Prove that the sum of all the matrices
>> is 0 i.e.,the zero matrix.
If any matrix in the group has a determinant which is equal to
neither one nor to minus one, then the group could not be finite.
So the absolute value of the determinant of every matrix in the
group must be one. I can't tell right off if the group would
have to be cyclic or commutative.
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