An inequality for selfadjoint operators on a Hilbert space
An inequality for selfadjoint operators on a Hilbert space
An elementary inequality of use in testing convergence of eigenvector calculations is proven. If <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="e Subscript lamda"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>e</mml:mi> <mml:mi>λ<!-- λ --></mml:mi> </mml:msub> </mml:mrow> <mml:annotation encoding="application/x-tex">{e_\lambda }</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a unit eigenvector corresponding to an eigenvalue <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="lamda"> …