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From: weemba@brahms.BERKELEY.EDU (Matthew P. Wiener)
Newsgroups: net.math
Subject: Re: I need an A in linear algebra!  Help!
Message-ID: <12350@ucbvax.BERKELEY.EDU>
Date: Thu, 13-Mar-86 03:53:48 EST
Article-I.D.: ucbvax.12350
Posted: Thu Mar 13 03:53:48 1986
Date-Received: Fri, 14-Mar-86 06:10:54 EST
References: <967@nmtvax.UUCP>
Sender: usenet@ucbvax.BERKELEY.EDU
Reply-To: weemba@brahms.UUCP (Matthew P. Wiener)
Distribution: net
Organization: University of California, Berkeley
Lines: 21
Summary: Good luck.

In article <967@nmtvax.UUCP> patrick@nmtvax.UUCP writes:
>Given matrix A of the form below, there are at most 4 matrices M1, M2, M3 and
>M4, such that Mi*Mi = I (M sub i squared is the identity matrix), and
>M1*M2*M3*M4 = A.  The "A" matrix is:
>[K 0 0 ..   0    ]                     [2  0]
>[0 K 0 ..   0    ]  and in particular  [0 .5]
>[. 0 K 0.   0    ]
>[. . 0 K    0    ]
>[.....0 1/k^(n-1)]
>   etc, and the nth row, nth column entry is 1/K^(n-1).
>The determinant of these beasts is 1.

The problem does not make sense as stated.  "There are at most 4 matrices",
for example, would make sense if the problem continued "M such that p(M)
holds", where p(.) is some property.  And if there is a quadruple of matrices
with the asked for properties, then there are infinitely many quadruples,
since any special orthogonal transformation, that is, replacing each Mi by
O*Mi*inv(O), where O is a special orthogonal matrix, preserves the asked
for property.

ucbvax!brahms!weemba	Matthew P Wiener/UCB Math Dept/Berkeley CA 94720