L∞ norm equals max absolute value
Image: Unknown; part of Brady-Handy Photograph Collection., Public domain, via Wikimedia Commons
Norm (mathematics)
L∞ norm equals max absolute value
The L∞ norm is defined as the maximum absolute value of the vector components. This norm measures the greatest deviation from zero among all components of the vector.
Example
For the vector (3, -7), the L∞ norm is 7, since 7 is the absolute value of the component with the greatest magnitude.
Understanding the L∞ norm is crucial for analyzing vector spaces and functions in various mathematical and engineering applications.
Related concepts
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
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
Matrix norm
L1 norm of a vector is the sum of absolute values of its components
Nyquist–Shannon sampling theorem
Sample at ≥ 2× the highest frequency to avoid aliasing
Chebyshev's inequality says: P(|X-μ| ≥ kσ) ≤ 1/k²
Chebyshev's inequality states: P(|X-μ| ≥ kσ) ≤ 1/k²
the L1 unit ball is a diamond shape and the L2 unit ball is a circle
L1 ball: Manhattan distance, L2 ball: Euclidean distance. Diamond shape for L1 reflects Manhattan geometry, circle for L2 reflects Euclidean geometry
One email a day: 5 concepts + the 5 stories that matter →
Swipe through 100 ML concepts daily
Open TickerNews