Hi, folks(adsbygoogle = window.adsbygoogle || []).push({});

I have had a hard time to find out whether or not there is a theorem in Linear Algebra or Spectral Theory that makes any strong statement about the relationship between the entries of a Matrix and its Eigenvalues and Eigenvectors.

Indeed, I would like to know how is the dependence between a matrix entries and its eigenvalues / eigenvectors. It could be something describing:

- what are the properties of the eigenvalues and eigenvectors of a matrix whose entries are less than 1 and greater than 0.

- what are the properties of the eigenvalues and eigenvectors of a matrix whose entries modulus are less than 1

- what are the properties of the eigenvalues and eigenvectors of a matrix whose entries goes to infinity

I'm studying spectral decomposition of matrices and would like to predict what will happen with the eigenvectors, given a diferent set of values for the Matrix entries.

I would appreciate any valuable reference with hints on that.

Regards,

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# Eigenvalues / Eigenvectors relationship to Matrix Entries Values

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