Euclidean norm

Linear algebra · Formula · Appears in 4 lessons

∥x∥2=∑i=1nxi2\|\mathbf{x}\|_2 = \sqrt{\sum_{i=1}^{n} x_i^2}

The straight-line length of a vector, straight out of Pythagoras. It is the default meaning of "how big" for a vector, and the quantity that gradient clipping, weight decay and distance metrics are all written in terms of.

Symbols

x\mathbf{x}
The vector being measured.
xix_i
Its i-th component.
nn
The number of dimensions.
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