Field of Values and Eigenvalues - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-23T05:31:45Z http://mathoverflow.net/feeds/question/64417 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/64417/field-of-values-and-eigenvalues Field of Values and Eigenvalues fkenter 2011-05-09T17:39:59Z 2011-05-09T17:39:59Z <p>Let $A$ be an $n \times n$ matrix. Define the field of values of $A$, denoted $W(A)$, as </p> <p>$W(A) := \{c \in \mathbb{C} : \exists x \in \mathbb{C}^n, \|x\|_2 = 1, x^H Ax = c \}$</p> <p>The question is, suppose one knows the spectra and singular values of $A$, are there any nontrivial bounds for the distance between an eigenvalue $\lambda$ and the edge of the field of values $\partial W(A)$?</p>