# Generalized set of Pauli elements for a basis for the linear transformations on the vector space [duplicate]

I have been doing some practice problems from "Gentle introduction to Quantum Computing". I am a little bit lost with this one:

The generalized Pauli group $$\mathcal G_n$$ is defined by all elements of $$\mathcal G_n$$ being of the form $$\mu A_1\otimes A_2 \otimes \ldots\otimes A_n$$ where $$A_j\in\left\lbrace I, X, Y, Z\right\rbrace$$ and $$\mu\in\left\lbrace 1, i, -1, -i\right\rbrace$$.

Show that generalized set of Pauli elements for a basis for the linear transformations on the vector space associated with an n-qubit system.

Is there any formal proof for this problem? And how do I approach it?

• +1. But what is meant here by "THE generalized set of Pauli elements"? – user1271772 May 29 '20 at 21:39