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BellaJ

Does this function preserve the norm of the individual vectors ? It does not look like it. Is it supposed to for liner functions?

keenan

@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?

BellaJ

@keenan Oh yes I understand now. Shear is not norm preserving. Other linear transformations that are norm preserving is rotation and translation.

keenan

@BellaJ Except that translation is not linear! :-) But otherwise, yes. Translations preserve distances between points.