The signature of a non-degenerate quadratic form
 |
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 
is allowed to be degenerate, one may write
 |
where the nonzero components 
square to zero. 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 
.
