Editing Metric signature (section)

== How to compute the signature ==
There are some methods for computing the signature of a matrix.
* For any [[nondegenerate]] [[Symmetric matrix|symmetric]] {{nowrap|''n''&thinsp;×&thinsp;''n''}} matrix, [[Matrix diagonalization|diagonalize]] it (or find all of [[eigenvalue]]s of it) and count the number of positive and negative signs.
* For a symmetric matrix, the [[characteristic polynomial]] will have all real roots whose signs may in some cases be completely determined by [[Descartes' rule of signs]].
* Lagrange's algorithm gives a way to compute an [[orthogonal basis]], and thus compute a diagonal matrix congruent (thus, with the same signature) to the other one: the signature of a diagonal matrix is the number of positive, negative and zero elements on its diagonal.
* According to Jacobi's criterion, a symmetric matrix is positive-definite if and only if all the [[determinant]]s of its main minors are positive.