Here are some examples of 2 dimensional transforms and their corresponding 2x2 matrices.
I have noted whether the matrix is symmetric or anti-symmetric across the leading diagonal. As you can see, rotation is anti-symmetric across the leading diagonal but symmetric along the diagonal, reflection is symmetric across the leading diagonal but anti-symmetric along the diagonal. This is not necessarily the case for 3D transforms here.
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Identity (symmetric) |
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Scale (symmetric) |
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Swap x and y axes, which is the same as reflecting in a 45° line (symmetric) |
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Swap x and y axes and invert y, which is the same as rotating by 90° (anti-symmetric) |
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Rotate by angle θ (anti-symmetric - but symmetric along the leading diagonal) |
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Reflection in x axis | ||||
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Reflection in line x,y (see this page) (symmetric - but anti-symmetric along the leading diagonal) |
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