Transforming to and From a Basis
n
Given
v
of dimension
n
and orthonormal basis
vectors
b
1
,
b
2
,..,
b
n
we can express v in this new
basis as
w
=
v
[
b
1
,
b
2
,..,
b
n
] = [
v
.
b
1
,
v
.
b
2
,..,
v
.
b
n
]
without loss of information