H

Hadamard product Given two m × n matrices A = (aij ) and B = (bij ), the Hadamard product (or Schur product) of A and B is their entrywise product, usually denoted by

A ◦ B = (aij bij ) .

half-angle formulas The trigonometric identities cos2 θ = (1 + cos(2θ))/2 and sin2 θ = (1 + cos(2θ))/2. half-side formulas Suppose that α, β, and γ are the angles of a spherical triangle. Denote by a the side of the triangle that is opposite α, and put S = (α + β + γ )/2 and

R = √

− cos S cos(S − α) cos(S − β) cos(S − γ ) .