sentences:  Then "W" is called an isotropic subspace of "V" if "some" vector in it is isotropic, a totally isotropic subspace if "all" vectors in it are isotropic, and an anisotropic subspace if it does not contain "any" (non-zero) isotropic vectors.The of a quadratic space is the maximum of the dimensions of the totally isotropic subspaces.A quadratic form "q" on a finite-dimensional real vector space "V" is anisotropic if and only if "q" is a definite form