Definition Three Most Popular p-Norms One norm:lxh=∑x↓ Two (or Euclidean)norm: x2=Vx好=VxHx Infinity (or maximum)norm: |xo=max1≤snl 色电年这大习 Matrix Theory Vector Norms -8/39
Definition Three Most Popular p-Norms One norm: ∥x∥1 = ∑ n j=1 ∣x∣j . Two (or Euclidean) norm: ∥x∥2 = √ ∑ n j=1 ∣x∣ 2 j = √ x Hx. Infinity (or maximum) norm: ∥x∥∞ = max1≤j≤n ∣xj ∣. Matrix Theory Vector Norms - 8/39
Definition Exercise If x=(1 2...n)TeR,then 命电有这女 Matrix Theory Vector Norms -9/39
Definition Exercise If x = ( 1 2 . . . n ) T ∈ R n , then ▸ ∥x∥1 = ▸ ∥x∥2 = ▸ ∥x∥∞ = Matrix Theory Vector Norms - 9/39
Definition Exercise If x=(1 2 ..n)eR,then Ixh 奇电有这头 Matrix Theory Vector Norms -9/39
Definition Exercise If x = ( 1 2 . . . n ) T ∈ R n , then ▸ ∥x∥1 = ▸ ∥x∥2 = ▸ ∥x∥∞ = Matrix Theory Vector Norms - 9/39
Definition Exercise If x=(1 2...n)eR,then lxl1=2(n+1) 奇电有这头子 Matrix Theory Vector Norms -9/39
Definition Exercise If x = ( 1 2 . . . n ) T ∈ R n , then ▸ ∥x∥1 = 1 2 n(n + 1) ▸ ∥x∥2 = ▸ ∥x∥∞ = Matrix Theory Vector Norms - 9/39
Definition Exercise Ifx=（12.n)eR",then lx1=2n(n+1) x2= 奇电有这头 Matrix Theory Vector Norms -9/39
Definition Exercise If x = ( 1 2 . . . n ) T ∈ R n , then ▸ ∥x∥1 = 1 2 n(n + 1) ▸ ∥x∥2 = ▸ ∥x∥∞ = Matrix Theory Vector Norms - 9/39