qSingular values are good
measures of the “size” of the matrix singular vectors are good
indications of strong/weak input or output directions.

Geometrically,
the singular values of a matrix *A* are precisely the lengths of the semi-axes
of the hyperellipsoid *E* defined by

Thus *v**1* is the
direction in which ||*y*||
is largest for all ||*x*||=*1*, while *v**n* is the direction in which ||*y*|| is smallest for all ||*x*||=*1*

• e.g.,

•