Thank you very much!
Some webpages say that the signature of a symmetric real matrix is an integer which equals to the number of positive eigenvalues minus the number of negative ones.
However, I am confused by one problem (Problem 4.1.23, Sp81 on Berkeley Problems in Mathematics):
The set of real $3 \times 3$ symmetric matrices is a real, finite-dimensional vector space isomorphic to $\mathbb{R}^6$. Show that the subset of such matrices of signature $(2,1)$ is an open connected subspace in the usual topology on $\mathbb{R}^6$.
So, what are matrices "of signature $(2,1)$", and what is the signature of a matrix?
Many thanks!
