Suppose we have a square matrix $A$. Under what conditions on $A$ ensure that all eigenvalues of $A$ are finite?
2026-04-12 16:59:14.1776013154
Under what conditions are the eigenvalues of a matrix finite?
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I don't believe I've heard of an infinite eigenvalue before. If the field of scalars involved is the field of real numbers or of complex numbers, then an eigenvalue is a real or complex number, and all of those are finite. Only if there were such a thing as an infinite scalar could there be an infinite eigenvalue. There are fields with elements that are in some sense infinite, but you'd need to explain which sorts of fields of scalars you're talking about before anyone's likely to say much.
Perhaps you have in mind that the set of eigenvalues might be unbounded. If the eignevalues of an infinite matrix are $1,2,3,4,5,\ldots$, then there is no upper bound on the set of eigenvalues. But each individual eigenvalue is still finite. When the matrix has only finitely many entries, that sort of thing does not happen.