Linear Transformations

?
What are invariant points/lines?
Points/lines which are mapped onto themselves
1 of 16
Reflection in y axis
-1 0
0 1
2 of 16
Reflection in x axis
1 0
0 -1
3 of 16
Reflection in y = x
0 1
1 0
4 of 16
Reflection in y = -x
0 -1
-1 0
5 of 16
For transformation M, det M =
Scale factor
6 of 16
For transformation PQ,
Q followed by P
7 of 16
A 0
0 B
Stretch scale factor A parallel to the x-axis and scale factor B parallel to the y-axis
8 of 16
For A 0
0 B,
x and y axis are invariant lines and origin is invariant point
9 of 16
Reflection in plane x = 0
-1 0 0
0 1 0
0 0 1
10 of 16
Reflection in plane y = 0
1 0 0
0 -1 0
0 0 1
11 of 16
Reflection in z = 0
1 0 0
0 1 0
0 0 -1
12 of 16
Rotation θ anticlockwise about x axis
1 0 0
0 cos θ -sin θ
0 sin θ cos θ
13 of 16
Rotation θ anticlockwise about y axis
cos θ 0 sinθ
0 1 0
-sinθ 0 cosθ
14 of 16
Rotation θ anticlockwise about z axis
cos θ -sin θ 0
sinθ cos θ 0
0 0 1
15 of 16
Transformation A^-1
Reverses transformation A
16 of 16

Other cards in this set

Card 2

Front

Reflection in y axis

Back

-1 0
0 1

Card 3

Front

Reflection in x axis

Back

Preview of the front of card 3

Card 4

Front

Reflection in y = x

Back

Preview of the front of card 4

Card 5

Front

Reflection in y = -x

Back

Preview of the front of card 5
View more cards

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