Does this function preserve the norm of the individual vectors ? It does not look like it. Is it supposed to for liner functions?
@BellaJ You asked two questions here:
1) Are all linear transformations norm-preserving?
2) Are shears in particular norm-preserving?
Can you answer these questions yourself? For instance, what happens when you write out the matrix for a shear, apply it to a vector, and take the norm of that vector? Is it the same as the norm of the original vector? Can you give me an example of a linear transformation (other than the identity) that is norm-preserving?
@keenan Oh yes I understand now. Shear is not norm preserving. Other linear transformations that are norm preserving is rotation and translation.
@BellaJ Except that translation is not linear! :-) But otherwise, yes. Translations preserve distances between points.