Don't understand this reasoning with respect to linear operators.(adsbygoogle = window.adsbygoogle || []).push({});

Let S and T be linear operators on the finite dimensional vector space V. Then assuming the composition ST is invertible, we get

[tex]\text{null} \; S \subset \text{null} \; ST [/tex]

Why is that? I thought hard about it but I simply cannot follow. Is it not possible to have an element x of V that is in the nullspace of S but not in the nullspace of ST ? i.e. S maps x to 0 but T maps x to y where S don't map y to 0 ?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Don't understand this simple vector space problem

**Physics Forums | Science Articles, Homework Help, Discussion**