semi-norm

semi-norm englanniksi

1. A function denoted ∥''v''∥ that maps a vector ''v'' to a non-negative value such that ∥''cv''∥ = |''c''|.∥''v''∥, where ''c'' is a scalar, and ∥''v'' + ''w''∥ ≤ ∥''v''∥ + ∥''w''∥ (the inequality); the condition that ∥''v''∥ = 0 implies that ''v'' = 0 is not required, but when it holds, the semi-norm is a norm.