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Algebra

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Joined:	18 Dec 2007
Post:	926

7 Mar 2009 21:57:25 IST

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Solve this tough eigenvalue problem !!!

None

Consider the ( n+1) * (n+1) matrix A with the elements given by

aij = -1 if i=j

= i/n if j= i + 1 for i = 1 to n

= 1-(i-2)/n if j=i-1 for i = 2 to n+1

= 0 otherwise

So that sum of the elements in each column = 0

Prove that its eigenvalues are given by { 0, -2/n, -4/n , -6/n, ... , -2 }

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abhishek sinha

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Joined: 18 Dec 2007

Posts: 926

9 Mar 2009 21:33:14 IST

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not a single attempt till now (even by experts) !!!

Surprising .....

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