Most of these are matrix operators for 2-space; there are a few for 3-space at the end.
| Orthogonal projections |
Orthogonal projection onto the x-axis |
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| Orthogonal projection onto the y-axis |
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Orthogonal projection onto the line through the origin making an angle θ with the positive x-axis |
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| Reflections |
Reflection in the x-axis |
Reflection in the y-axis |
Reflection in the line y = x |
Reflection in the line through the origin making an angle θ with the positive x-axis |
| Scale changes |
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Horizontal expansion |
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Horizontal contraction |
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Vertical expansion |
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Vertical contraction |
| Shears |
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Horizontal shear with a positive factor |
| Horizontal shear with a negative factor |
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Vertical shear with a positive factor |
| Vertical shear with a negative factor |
| Rotations |
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Rotation about the origin through angle θ |
| Simple matrix operators on 3-space |
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Projection onto the x-y plane |
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Projection onto the z-axis |
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Reflection in the x-y plane |
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Reflection in the z-axis |
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Rotation about the z-axis through angle θ |
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