Vector norms

  • multiple measures of the size of vectors and matrices
  • norms are positive, scalar, and obey the triangle inequality (sum of the norms \(\geq\) norm of the sums)
  • vectors with norm 1 are unit vectors
  • usually 2-norm is implied
  • Magnitude direction form of a vector \(\mathbf{v}\):

\[ \mathbf{v} = ||\mathbf{v}|| \frac{\mathbf{v}}{||\mathbf{v}||} \]