The quadratic form signature of a non-degenerate quadratic form on a real vector space
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of rank 
is most often defined to be the ordered
pair 
of the numbers of positive, respectively negative,
squared terms in its reduced form.
In the event that the quadratic form 
on a real vector space
is allowed to be degenerate, one may write
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where the last 
coordinates have zero coefficients
in 
.
In this case, the signature of 
is most often denoted by one of the triples 
or 
.
A number of other, less common definitions are sometimes attributed to a quadratic form as its signature. In particular, the signature of 
is sometimes defined to be the number 
of positive squared terms in
its reduced form, as well as the quantity 
.
