The following applet exhibits the change in the matrix representation of a linear transformation with a change in basis.
Let
be
defined by
Let
and
i) Matrix of
with respect to
:
and
i.e.
.
Hence
.
ii) Matrix
with respect to
:
iii) Matrix of change of basis from
to
:
iv) Matrix
for change of basis from
to
:
| -:- |