Norm

Norm

  • Defines the measure of the length of a vector

Definition #

A norm is a non-negative function norm_be90dd13aedd9eb75d464a8b0c4e637ff1a038ff.svg that fullfills these requirements:

  1. Triangle inequality: norm_fb0a7231631ebba615b35533f3e5401f5f7f9fd2.svg
  2. norm_5c64534e338ea9f2c53a189e9d24e24b5a6e9e7b.svg for scalar norm_436556cb15c4ea9bea0d7b8d49f53943856148d8.svg
  3. norm_85434657dd8a71b34ee10ff8fb3bf72ef1a8ae47.svg

L1-Norm #

Also knows as the Taxicab distance or Manhattan distance Writen as norm_fd878226a2b6d7b5e4eec3ffbd7fc8c89476eeb8.svg and defined as: norm_b82fd4df1e179e2c6ab7fd1b34e31adbb19d9d69.svg

L2-Norm #

The typical euclidian distance as we know and love it. Written as norm_73292b80181c9fb4f76f7d70c0f69f53802f0a60.svg and defined as: norm_b52aecd9c5869854dc4c2fc4c85070a6ee4610d8.svg

Lp-Norm #

We can define the Lp-Norm for any norm_1e07f5ea8054cbe9e33803f209e513c65026fcf2.svg as follows: norm_e1dfdb045d5d3a429be288253a1c58c83da1291b.svg

Calendar October 22, 2023