We know for multicovectors wedge product hs the bilinearity property:
$(aw + a' w')\wedge \eta = a(w\wedge \eta)+ a'(w'\wedge \eta)$
The problem is: does here need $w,w'$ to be the same grad i.e. both of them are k-covectors?
When we talk about exterior algebra ,we construct $\Lambda\left(V^{*}\right)=\bigoplus_{k=0}^{n} \Lambda^{k}\left(V^{*}\right)$ then what is the meaning of the sum here? And why they are disjoint?