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I am trying to calculate the characteristic polynomial of the matrix $n\times n$, $A=\{a_{ij}=1\}$.

When $n=2$, I obtained $p(\lambda)=\lambda^2-2\lambda$ .

In the case $n=3$, $p(\lambda)=-\lambda^3+3\lambda^2$.

For $n=4$, $p(\lambda)=\lambda^4 - 4\lambda^3$.

I guess that for the general case, we have $p(\lambda)=(-1)^n\lambda^{n}+(-1)^{n-1}n\lambda^{n-1}$.

I tried to use induction, but it didn't work, unless I've done wrong

Somebody can help me or give me a hint

  • 0
    I think it's easier to just compute all of the eigenvalues. The eigenvectors are easy to write down. (Also, you should be using a definition of the characteristic polynomial that makes it monic.)2012-06-03
  • 0
    I really dont understand the problem, could any one explain me?2012-06-06
  • 0
    Also see https://math.stackexchange.com/questions/2853981/find-the-eigenvalues-and-their-multiplicities-of-a-special-matrix?noredirect=1&lq=12018-07-17

3 Answers 3