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:
“No man, not even a doctor, ever gives any other definition of what a nurse should be than this—”devoted and obedient.” This definition would do just as well for a porter. It might even do for a horse. It would not do for a policeman.”
—Florence Nightingale (1820–1910)
“I’m beginning to think that the proper definition of “Man” is “an animal that writes letters.””
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)
“Was man made stupid to see his own stupidity?
Is God by definition indifferent, beyond us all?
Is the eternal truth man’s fighting soul
Wherein the Beast ravens in its own avidity?”
—Richard Eberhart (b. 1904)