Difference between revisions of "Indefinite metric"
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| − | A term used in the theory of spaces with an indefinite metric (cf. [[Space with an indefinite metric|Space with an indefinite metric]]) for denoting (depending on the type of space) either a [[Bilinear form|bilinear form]], a [[Sesquilinear form|sesquilinear form]] or a (non-linear) functional of a certain degree of homogeneity, defined on the space under consideration. An indefinite metric is not a metric (that is, a distance), and the epithet "indefinite" means that either the sesquilinear form is not positive definite or the functional is not a power of a norm on the space. The various types of indefinite metrics are called | + | {{TEX|done}} |
| + | A term used in the theory of spaces with an indefinite metric (cf. [[Space with an indefinite metric|Space with an indefinite metric]]) for denoting (depending on the type of space) either a [[Bilinear form|bilinear form]], a [[Sesquilinear form|sesquilinear form]] or a (non-linear) functional of a certain degree of homogeneity, defined on the space under consideration. An indefinite metric is not a metric (that is, a distance), and the epithet "indefinite" means that either the sesquilinear form is not positive definite or the functional is not a power of a norm on the space. The various types of indefinite metrics are called $G$-metric, $I$-metric, $J$-metric (see [[Hilbert space with an indefinite metric|Hilbert space with an indefinite metric]]; [[Pontryagin space|Pontryagin space]]). | ||
Latest revision as of 10:45, 16 April 2014
A term used in the theory of spaces with an indefinite metric (cf. Space with an indefinite metric) for denoting (depending on the type of space) either a bilinear form, a sesquilinear form or a (non-linear) functional of a certain degree of homogeneity, defined on the space under consideration. An indefinite metric is not a metric (that is, a distance), and the epithet "indefinite" means that either the sesquilinear form is not positive definite or the functional is not a power of a norm on the space. The various types of indefinite metrics are called $G$-metric, $I$-metric, $J$-metric (see Hilbert space with an indefinite metric; Pontryagin space).
How to Cite This Entry:
Indefinite metric. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Indefinite_metric&oldid=18743
Indefinite metric. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Indefinite_metric&oldid=18743
This article was adapted from an original article by A.I. Shtern (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article