Let A be an (n x n) upper Hessenberg matrix with the following constraints:(adsbygoogle = window.adsbygoogle || []).push({});

a_{j,j} < 0 , j=1,...,n

a_{j,j}= - sum a_{i,j} [i≠j] , j=1,...,n-1

a_{n,n} > - sum a_{i,n} [i≠n]

Example:

-1 2 0 2 0

1 -5 4 0 0

0 3 -9 1 0

0 0 5 -5 3

0 0 0 2 -7

I want to prove A is diagonalizable (I am pretty sure it is, but haven't

found a formal demostration)

Hint: If we make a_{1,4}=0; a_{4,4}=-3, then it is a tridiagonal matrix

similar to a Hermitian one, and therefore diagonalizable.

Thanks for your help,

_M.

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# Upper Hessenberg zero-column sum matrix

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