It is logical that the inverse of a linear transformation encodes the reverse linear transformation. However, some transformations are also non-invertible - and so we have to use the pseudoinverse to "undo" a particular scaling, rotation, or other linear transformation. Does taking the pseudoinverse of a 2D-H transformation matrix also undo that transformation? I don't see too much material on this topic online.
Gyro
From my understanding, all linear transform matrices are invertible because we cannot find a single case where we can make a linear transform matrix with determinant zero.
And taking a pseudoinverse of a non-invertible matrix will not always reverse the transform. For example, if it's an orthogonal projection transformation, it will lose one dimension which makes impossible to be reversed later.
tbell
What about scaling by 0, or some sort of degenerate shear that collapses space to a line? Those would be linear transformations with determinant zero.
It is logical that the inverse of a linear transformation encodes the reverse linear transformation. However, some transformations are also non-invertible - and so we have to use the pseudoinverse to "undo" a particular scaling, rotation, or other linear transformation. Does taking the pseudoinverse of a 2D-H transformation matrix also undo that transformation? I don't see too much material on this topic online.
From my understanding, all linear transform matrices are invertible because we cannot find a single case where we can make a linear transform matrix with determinant zero.
And taking a pseudoinverse of a non-invertible matrix will not always reverse the transform. For example, if it's an orthogonal projection transformation, it will lose one dimension which makes impossible to be reversed later.
What about scaling by 0, or some sort of degenerate shear that collapses space to a line? Those would be linear transformations with determinant zero.