Index of a Symmetric Matrix In Hansjorg Geiges' introductory textbook on Symplectic Geometry, is defined a projective conic given by $q^tAq=0$ where $A$ is a symmetric matrix of rank 3 and index 2. What does "index 2" mean? I googled it in vain. I am seeing the term "index of a matrix" for the very first time. It was not taught to me either. The reason I want to know is that I would like to plug some value for A and visualise the projective conic given in the text. Any help is greatly appreciated.
Index of real quadratic form x'Axmeans number of 1  s in canonical reduction .It  is same as number of  positive eigen values of real symmetric matrix A.
Index of real quadratic form x'Axmeans number of 1  s in canonical reduction .It  is same as number of  positive eigen values of real symmetric matrix A.