Linear Transformations

1 0
0 -1

Reflection through x1

-1 0
0 1

Reflection through x2

0 1
1 0

Reflection through x2=x1

0 -1
-1 0

Reflection through x2=-x1

k 0. k<1
0 1

Horizontal Contraction

k 0 k>1
0 1

Horizontal Stretch

1 0 k<1
0 k

Vertical Contraction

1 0 k>1
0 k

Vertical Stretch

1 k k<0
0 1

Left Shear

1 k k>0
0 1

Right Shear

1 0
0 0

Projection to x1

0 0
0 1

Projection to x2