Spectrum (linear operator)/Definition: Difference between revisions

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A definition or brief description of Spectrum (linear operator).

A set of values {λ} characteristic of an operator O mapping a Banach space into itself such that O x_λ = λ x_λ for some nonzero vectors x_λ.

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	<noinclude>{{Subpages}}</noinclude>A set of values {λ} characteristic of an operator ''O'' mapping a [[Banach space]] into itself such that {{nowrap\|''O x<sub>λ</sub>''<nowiki> =</nowiki> ''λ x<sub>λ</sub>'' for some nonzero vectors ''x<sub>λ</sub>''.		<noinclude>{{Subpages}}</noinclude>A set of values {λ} characteristic of an operator ''O'' mapping a [[Banach space]] into itself such that {{nowrap\|''O x<sub>λ</sub>''<nowiki> =</nowiki> ''λ x<sub>λ</sub>''}} for some nonzero vectors ''x<sub>λ</sub>''.