Definition Definition A vector norm is a function from Ch to R with three properties: Nonnegative:llxl≥0 for all x∈Cn, xI=0 if and only if x =0. 命电有这女子 Matrix Theory Vector Norms -5/39Definition Definition A vector norm ∣∣ ⋅ ∣∣ is a function from C n to R with three properties: Nonnegative: ∣∣x∣∣ ≥ 0 for all x ∈ C n , ∣∣x∣∣ = 0 if and only if x = 0. Homogeneous: ∣∣αx∣∣ = ∣α∣∣∣x∣∣ for all α ∈ C, x ∈ C n . Triangle inequality: ∣∣x + y∣∣ ≤ ∣∣x∣∣ + ∣∣y∣∣ for all x, y ∈ C n . Matrix Theory Vector Norms - 5/39