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 $\mathbf{v}$:

$$\mathbf{v} = ||\mathbf{v}|| \frac{\mathbf{v}}{||\mathbf{v}||}$$