L1 norm of a vector is the sum of absolute values of its components
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Matrix norm
L1 norm of a vector is the sum of absolute values of its components
The L1 norm, also known as the Manhattan norm, represents the sum of the absolute values of the components of a vector. It measures the distance from the origin to the point in a grid-like path, akin to navigating city blocks.
Example
For a vector v = [3, -4, 2], the L1 norm is calculated as |3| + |-4| + |2| = 3 + 4 + 2 = 9.
Understanding the L1 norm is crucial for applications in optimization and machine learning, where it helps measure distances and errors.
Related concepts
Normalization (machine learning)
L2 normalization equation: x_i' = x_i / ||x||_2
Dot product
Dot product = sum of products of corresponding entries
Norm (mathematics)
L∞ norm equals max absolute value
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
Regression analysis
Linear regression equation: ŷ = β0 + β1X
Quadratic equation
Quadratic equation standard form: ax² + bx + c = 0
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