A binary relation is an equivalence relation if it is reflexive, transitive, and has, for 10 points, what property that also describes a square matrix in which the i,j-th entry equals the j,i-th entry, so that it equals its own transpose?
Sylvester's Law of Inertia implies that a bilinear form of this type has unique index and signature. For a topological group, a neighborhood is said to be of this type if it equals its own inverse. For a pair of sets, the difference of this type is equivalent to the logical exclusive or. (*) Cayley's Theorem states that any finite group of order n is isomorphic to some subgroup of the degree-n group of this type. A real matrix is of this type if and only if it is orthogonally equivalent to a real diagonal matrix. The degree-n group of this type contains as a normal subgroup the alternating group of degree n, and consists of permutations on n objects. A binary relation is an equivalence relation if it is reflexive, transitive, and has, for 10 points, what property that also describes a square matrix in which the i,j-th entry equals the j,i-th entry, so that it equals its own transpose?
Sylvester's Law of Inertia implies that a bilinear form of this type has unique index and signature.
{symmetric} [accept {symmetry} or other word forms]