41. In a vector space of finite dimension, a vector hyperplane is thus a subspace of dimension. 42. A hyperplane on a topological vector space " X " is either dense or closed. 43. It's kernel, which is a hyperplane passing through the origin, and its norm. 44. The reflection of a point " x " about this hyperplane is the linear transformation: 45. Be sure to note that the vector \ vec w is the normal to the discriminant hyperplane . 46. Large values of the communalities will indicate that the fitting hyperplane is rather accurately reproducing the correlation matrix. 47. In particular, the root system must be invariant under reflection through the hyperplane perpendicular to any root. 48. The topology of hyperplane sections is studied in the topic of the Lefschetz hyperplane theorem and its refinements. 49. The topology of hyperplane sections is studied in the topic of the Lefschetz hyperplane theorem and its refinements. 50. There are more than one hyperplane separating a closed convex set and a point lying outside of it.
