Let us consider the transformation of a vector OP
from (x,y) (referred to as old) Cartesion
coordinates system to (x', y') (new) system.
Or,
inverting
Above
represents a transformation of coordinates when the system is rotated at an
angle q CCW
2B1
Tensors
Let
be
two vectors in a Cartesian coordinate system. If
is
a transformation, which transforms any vector into some other vector, we can
write
where
and
are
two different vectors.
For
any arbitrary vector
and
and scalar
,
then
is called a Linear Transformation or a Second Order
Tensor.
(1.1a) and (1.2a) can be written as,
