A real, nondegenerate 
symmetric matrix 
, and its corresponding symmetric
bilinear form 
,
has signature 
if there is a nondegenerate matrix 
such that 
is a diagonal matrix with 
1s and 
s.
In this case, 
is a diagonal quadratic form.
For example,
![A=[1 0 0 0; 0 1 0 0; 0 0 1 0; 0 0 0 -1]](/images/equations/MatrixSignature/NumberedEquation1.svg) |
gives a symmetric bilinear form 
called the Lorentzian
inner product, which has signature 
.
