O'Reilly logo

The Manga Guide to Linear Algebra by Ltd. Trend-Pro Co., Iroha Inoue, Shin Takahashi

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

Crdinates 161
Coordinates
Coordinates in linear algebra are a bit different from the coordinates explained
in high school. I’ll try explaining the difference between the two using the image
below.
O
x
2
4
7
x
1
O
u
2
x
2
1
2
u
1
x
1
x
O
point (7, 4)
point
0
1
+ 4
1
0
7
4
= 7
point (2, 1)
1
2
+ 1
3
1
7
4
= 2
When working with coordinates and coordinate systems at the high school
level, it’s much easier to use only the trivial basis:
, ,
1
0
0
0
1
0
0
0
1
,
In this kind of system, the relationship between the origin and the point in
the top right is interpreted as follows:
O
x
2
4
7
x
1
O
u
2
x
2
1
2
u
1
x
1
x
O
point (7, 4)
point
0
1
+ 4
1
0
7
4
= 7
point (2, 1)
1
2
+ 1
3
1
7
4
= 2
162 Chapter 6 More Vectors
It is important to understand that the trivial basis is only one of many bases
when we move into the realm of linear algebraand that using other bases pro-
duces other relationships between the origin and a given point. The image below
illustrates the point (2, 1) in a system using the nontrivial basis consisting of
the two vectors
1
2
and u
2
=
3
1
u
1
=
.
This alternative way of thinking about coordinates is very useful in factor
analysis, for example.
O
x
2
4
7
x
1
O
u
2
x
2
1
2
u
1
x
1
x
O
point (7, 4)
point
0
1
+ 4
1
0
7
4
= 7
point (2, 1)
1
2
+ 1
3
1
7
4
= 2

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required