This preview shows pages 1–2. Sign up to view the full content.
SECTION 4.7 CHANGE OF BASIS
Calculations in physics and engineering problems sometimes become simpler when we
make good choices for the coordinate system, that is, the location of the origin and the
direction of the axes we use when we translate the problem into mathematics. In this
section we look at the eﬀect of changing the axes. In our terminology, this means we want
to change from one basis for a vector space to another basis for the same vector space. How
does this change the coordinates of a given vector?
A TWODIMENSIONAL EXAMPLE.
Now suppose we have a basis
B
for an
n
dimensional vector space
V
. Each vector
x
in
V
then has a
B
coordinate vector [
x
]
B
. Then we have
another
basis
C
, so each vector
x
in
V
then has a
C
coordinate vector [
x
]
C
. How do we get from one of these coordinate vectors
to the other?
Suppose
B
=
{
b
1
,
b
2
,
b
3
}
and [
x
]
B
=
r
1
r
2
r
3
. Now let’s calculate [
x
]
C
.
FACT.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '08
 PAVLOVIC
 Linear Algebra, Algebra

Click to edit the document details