the L1 norm is not differentiable at zero

Norm (mathematics)

L∞ norm equals max absolute value

Matrix norm

L1 norm of a vector is the sum of absolute values of its components

The elastic net combines L1 and L2: λ₁|w| + λ₂w² gives both sparsity and stability

Elastic net: λ₁|w| + λ₂w² enforces sparsity and stability simultaneously

the condition number κ(A) measures: sensitivity of Ax=b to perturbations

The condition number κ(A) measures the sensitivity of Ax=b to perturbations

Dynamical system

A fixed point is where dx/dt = 0

the Lp norm ball shape changes as p goes from 1 to 2 to infinity

As p increases from 1 to 2 to infinity, the Lp norm ball becomes more spherical