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

the L1 norm is not differentiable at zero

The L1 norm is not differentiable at zero because the absolute value function has a kink at zero

ill-conditioned matrices cause numerical instability: small input changes → large output changes

Ill-conditioned matrices amplify input perturbations, leading to significant output variability

Entropy H = -Σ p(x) log₂ p(x) measures average surprise in bits

Entropy H = -Σ p(x) log₂ p(x) quantifies uncertainty in a system

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

Lyapunov exponents measure: rate of divergence of nearby trajectories in a dynamical system

Lyapunov exponents measure the rate of divergence of nearby trajectories in a dynamical system

the dot product measures alignment: it equals |a||b|cos(θ)

Dot product measures alignment: it equals |a||b|cos(θ)