MetrikSignatur
MetrikSignatur, or metric signature, is a concept in real linear algebra and differential geometry that describes the pair (p, q) associated with a real symmetric bilinear form B on a finite-dimensional real vector space V. It records the numbers of positive and negative squares that appear in a diagonalized representation of B and indicates whether the metric is definite or indefinite.
Sylvester’s law of inertia states that for any real symmetric matrix representing B in any basis, the
Examples illustrate common signatures. The standard Euclidean inner product on R^n has signature (n, 0). The
In complex vector spaces, the notion of signature is less standard; positivity is usually discussed in terms