Linear Transformations
A linear transformation,
, is just a mapping from
V
to
V
which satifies the following properties:
Linearity implies:
Expressing
with a basis and coordinate vector gives:
Matrices are a common class of linear operators. Furthermore, when a matrix operator is applied to
any
vector the result,
, is an element of
V
. Thus,
Lecture 8
Slide 5
6.837 Fall '01
, is
just a mapping from V to V which satifies the following properties:
with a
basis and coordinate vector gives:
,
is an element of V. Thus,
