Sage and Linear Algebra Worksheet: FCLA Section ILT

Section 1 Injective Linear Transformations

Two carefully-crafted linear transformations: T is injective, S is not.

We create two different inputs, which differ by a random vector from the kernel (which we hope is not simply the zero vector, a distinct possibility). We always get the same output from S, predictably. If we try this with T then the kernel vector is always the zero vector and the demonstration is very uninteresting.