Product of diagonal elements of a square matrix
in [Math]
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From: Lily Selivan on 30 Jun 2010 09:44 Hello. I have a question on linear algebra. Is the product of diagonal elements of a square matrix the invariant? If it is true how to prove this? Thank you very much!
From: Ken Pledger on 30 Jun 2010 16:41 In article <100899668.29383.1277919887096.JavaMail.root(a)gallium.mathforum.org>, Lily Selivan <selivan0804(a)gmail.com> wrote: > .... > Is the product of diagonal elements of a square matrix the invariant? If it > is true how to prove this? .... Try some simple 2 x 2 examples. I think you'll pretty soon find that it's false. Ken Pledger.
From: Gerry Myerson on 30 Jun 2010 19:16 In article <ken.pledger-B972B1.08410201072010(a)62-183-169-81.bb.dnainternet.fi>, Ken Pledger <ken.pledger(a)mcs.vuw.ac.nz> wrote: > In article > <100899668.29383.1277919887096.JavaMail.root(a)gallium.mathforum.org>, > Lily Selivan <selivan0804(a)gmail.com> wrote: > > > .... > > Is the product of diagonal elements of a square matrix the invariant? If it > > is true how to prove this? .... > > > Try some simple 2 x 2 examples. I think you'll pretty soon find > that it's false. She won't find it true or false if she doesn't know what "invariant" means in this context, and I suspect that's the case, else, why ask the question? So, let's tell her; in this context, we say George is an invariant if the George value of A equals the George value of B-inverse A B for all A and all invertible B. -- Gerry Myerson (gerry(a)maths.mq.edi.ai) (i -> u for email)
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