How to understanding an any automorphism can be represented as a sum of even and odd ones in Dorfman's book?

Question

How to understand any automorphism can be represented as a sum of even and odd ones in Dorfman's book?

Answer 1

This is worded confusingly, it should be endomorphisms $\text{End}(Q)$ rather than automorphisms; automorphisms would form a group, not a Lie algebra.

The endomorphisms of a super vector space $V = V_0 \oplus V_1$ can be written in block form $X = \left[ \begin{array}{cc} X_{00} & X_{10} \\ X_{01} & X_{11} \end{array} \right]$ where $X_{ij}$ is the component that sends $V_i$ to $V_j$. The even part is the diagonal blocks $\left[ \begin{array}{cc} X_{00} & 0 \\ 0 & X_{11} \end{array} \right]$ and the odd part is the off-diagonal blocks $\left[ \begin{array}{cc} 0 & X_{10} \\ X_{01} & 0 \end{array} \right]$.