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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!!

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

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