Rotation using matrices

Another use for matrices is for rotating points or whole objects for example, in computer graphics.

For a given point:

(

x
y
z

)

or a whole object with multiple points:

(

x₁
y₁
z₁

x₂
y₂
z₂

x₃
y₃
z₃

...
...
...

)

These can be multiplied with one of these matrices to rotate it:

Around the X-axis

(

1
0
0

0
Cos (a)
-Sin (a)

0
Sin (a)
Cos (a)

)

(

Cos (a)
0
-Sin (a)

0
1
0

Sin (a)
0
Cos (a)

)

(

Cos (a)
-Sin (a)
0

Sin (a)
Cos (a)
0

0
0
1

)

Note that if you swap the signs on both sines, then the direction of rotation inverts.

If you just want to rotate a two-dimentional figure, use:

(

Cos (a)
-Sin (a)

Sin (a)
Cos (a)

)

Have you found an error or do you want to add more information to these pages?
You can contact me at the bottom of the home page.