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#1 2012-09-10 18:57:34
- yago.dorea
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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.
#2 2012-09-10 19:31:28
- bobbym
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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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#3 2012-09-10 19:46:56
- yago.dorea
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Re: Fibonacci's determinant
Ah I got it, you start from the beggining, I was doing the cofactors of the last terms... Thank you!
#4 2012-09-10 20:19:38
- bobbym
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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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#5 2012-09-10 21:07:44
- yago.dorea
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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.
#6 2012-09-10 21:18:05
- bobbym
- Administrator
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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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.