# Wedge product questions

I am getting initiated in the wedge product, and I'm trying to understand these properties:

1. Linearity$$\left(\lambda\omega^{p}\right)\land\omega^{q}=\omega^{p}\land\left(\lambda\omega^{q}\right)=\lambda\left(\omega^{p}\land\omega^{q}\right)$$ and $$\left(\omega_{1}^{p}+\omega_{2}^{p}\right)\land\omega^{q}=\omega_{1}^{p}\land\omega^{q}+\omega_{2}^{p}\land\omega^{q}$$
2. Anticommutativity

$$\omega^{p}\land\omega^{q}=\left(-1\right)^{pq}\omega^{q}\land\omega^{p}$$

1. Asociativity

$$\left(\omega^{p}+\omega^{q}\right)\land\omega^{r}=\omega^{p}+\left(\omega^{q}\land\omega^{r}\right)$$

I would like to know if someone can give me some intuitive ideas of why they work like that, because everywhere I look, or it says that is very simple and direct from the initial definition (wich often is very messy for me) or it has a very large proof wich has a lot of concepts and ideas that I haven't covered yet. So please I would love to hear what's the idea behind it. Thanks in advance!!

• Have you already been initiated into the tensor product? – KCd May 16 at 1:25
• @KCd no, I've only been introduced to differential forms and not too much in depth. – Jack Talion May 16 at 5:02
• What is the reference book in your course for this material? – KCd May 16 at 18:53