Definition
Let A be a symmetric matrix of reals. More generally, the metric signature (p, q, r) of A is a set of three natural numbers defined as the number of positive, negative and zero eigenvalues of the matrix counted with regard to their algebraic multiplicity. When r is nonzero the matrix A is called degenerate.
If φ is a scalar product on a finite-dimensional vector space V, the signature of V is the signature of the matrix that represents φ with respect to a chosen basis. According to Sylvester's law of inertia, the signature does not depend on the choice of basis.
Read more about this topic: Metric Signature
Famous quotes containing the word definition:
“The very definition of the real becomes: that of which it is possible to give an equivalent reproduction.... The real is not only what can be reproduced, but that which is always already reproduced. The hyperreal.”
—Jean Baudrillard (b. 1929)
“Although there is no universal agreement as to a definition of life, its biological manifestations are generally considered to be organization, metabolism, growth, irritability, adaptation, and reproduction.”
—The Columbia Encyclopedia, Fifth Edition, the first sentence of the article on “life” (based on wording in the First Edition, 1935)
“... if, as women, we accept a philosophy of history that asserts that women are by definition assimilated into the male universal, that we can understand our past through a male lens—if we are unaware that women even have a history—we live our lives similarly unanchored, drifting in response to a veering wind of myth and bias.”
—Adrienne Rich (b. 1929)