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signature -- outputs the signature of a symmetric bilinear form over the real or rational numbers



Given a symmetric bilinear form, after diagonalizing it, we can consider the number of positive entries minus the number of negative entries appearing along the diagonal. This is the signature of a symmetric bilinear form, and is one of the primary invariants we use to classify forms. For more information see gwIsomorphic.

i1 : M = matrix(RR,{{0,0,1},{0,1,0},{1,0,0}});

                3         3
o1 : Matrix RR    <-- RR
              53        53
i2 : beta = gwClass(M);
i3 : signature(beta)

o3 = 1

See also

Ways to use signature :

For the programmer

The object signature is a method function.