Editing Metric signature (section)

== Definition ==
The signature of a metric tensor is defined as the signature of the corresponding [[quadratic form]].<ref>{{cite book|last1=Landau|first1=L.D.|authorlink1=Lev Landau|last2=Lifshitz|first2=E.M.|authorlink2=Evgeny Lifshitz|title=The Classical Theory of Fields|series=Course of Theoretical Physics|volume=2|edition=4th|publisher=[[Butterworth&ndash;Heinemann]]|isbn=0-7506-2768-9|year=2002|orig-year=1939|pages=245&ndash;246}}</ref> It is the number {{nowrap|(''v'', ''p'', ''r'')}} of positive, negative and zero [[eigenvalues]] of any matrix (i.e. in any basis for the underlying vector space) representing the form, counted with their [[Algebraic multiplicity|algebraic multiplicities]]. Usually, {{nowrap|''r'' {{=}} 0}} is required, which is the same as saying a metric tensor must be nondegenerate, i.e. no nonzero vector is orthogonal to all vectors.

By Sylvester's law of inertia, the numbers {{nowrap|(''v'', ''p'', ''r'')}} are basis independent.