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From: JEMebius on 5 Jun 2010 17:32
JEMebius wrote:
> Kaba wrote:
>> Ron wrote:
>>> On Jun 5, 7:23 am, Kaba <n...(a)here.com> wrote:
>>>> Stephen Montgomery-Smith wrote:
>>>>> Kaba wrote:
>>>>>> Hi,
>>>>>> This is part of the first question for chapter 1 of "Applied
>>>>>> numerical
>>>>>> linear algebra" book, but I just can't come up with a solution:
>>>>>> If A and B are orthogonal matrices, and det(A) = -det(B), show that
>>>>>> A + B is singular.
>>>>>> Any hints?
>>>>> Here is my attempt. If A is orthogonal, then the determinant is
>>>>> either
>>>>> 1 or minus 1. WLOG det(A) = 1. Now
>>>>> A+B = A(I + A^{-1} B)
>>>>> so WLOG A=I, and B is an orthogonal matrix whose determinant is -1.
>>>> Could you be more specific why WLOG here?
>>>>
>>> I suspect the idea is this. A is invertible so A+B is singular if and
>>> only if I+A^{-1}B is singular. So we simply consider the case where
>>> A=I and B is an orthogonal matrix of determinant -1. The argument is
>>> essentially the same as the earlier one using the fact that an
>>> orthogonal matrix of determinant -1 has -1 as an eigenvalue.
>>
>> Ok, I see, it works:)
>>
>
>
> Typesetting tip: A^-1 instaed of A^(-1)
>
> The Thunderbird EMail/Newsgroup program interprets "^" (caret) as
> exponentiation.
> I guess all such programs do so.
>
> The string following "^" is converted to superscript as far as it looks
> like a number,
> positive or negative, integer or non-integer.
>
> My guess: any character other than 0 1 2 3 4 5 6 7 8 9 + - . stops the
> superscript mode.
>
> Check: A^0, A^+1, A^1, A^+1.2345, A^1.2345, A^-6, A^-6.7890, A^.5, A^-.5
>
> Johan E. Mebius


Apparently "+" and "." prevent superscript mode, thus spoiling the game - Johan E. Mebius
From: Kaba on 5 Jun 2010 22:14
JEMebius wrote:
> > Typesetting tip: A^-1 instaed of A^(-1)
> >
> > The Thunderbird EMail/Newsgroup program interprets "^" (caret) as
> > exponentiation.
> > I guess all such programs do so.

Hmm, I don't think this is standard, or common. For example, I am using
Microplanet Gravity, and it does not do this. I prepare my posts for
direct ascii consumption. That being said, I can try to format my
exponents without brackets in the future, when that is sufficient.

--
http://kaba.hilvi.org
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