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#1 2012-09-09 20:57:34

yago.dorea
Member
Registered: 2012-09-09
Posts: 6

Fibonacci's determinant

Hello, I want to prove that the determinant of Fibonacci's nxn tridiagonal matrix is equal to the (n+1)th term of the Fibonacci sequence.

I'm trying to do it by induction, stating that det(F(n)) = det(F(n-1)) + det(F(n-2)) (yeah I don't know how to use LaTex)
but I don't know how to prove that the minor M(n, n-1)(F(n)) = det(F(n-2))

Thanks.


Live long and prosper.

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#2 2012-09-09 21:31:28

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,444

Re: Fibonacci's determinant

Hi;

Try this pdf ( first page ) and see if any of it helps.

http://ocw.mit.edu/courses/mathematics/ … 0_soln.pdf


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#3 2012-09-09 21:46:56

yago.dorea
Member
Registered: 2012-09-09
Posts: 6

Re: Fibonacci's determinant

Ah I got it, you start from the beggining, I was doing the cofactors of the last terms... Thank you!


Live long and prosper.

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#4 2012-09-09 22:19:38

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,444

Re: Fibonacci's determinant

Hi yago.dorea;

Your welcome and welcome to the forum.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#5 2012-09-09 23:07:44

yago.dorea
Member
Registered: 2012-09-09
Posts: 6

Re: Fibonacci's determinant

I'm glad I found this forum. I am being amazed by some topics in the "Dark Discussions at Cafe Infinity" section. Mainly one article about the Vandermonde Determinant.


Live long and prosper.

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#6 2012-09-09 23:18:05

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,444

Re: Fibonacci's determinant

Hi yago.dorea;

Yes, there is good stuff here.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

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