I read the definition of wedge product here: http://mathworld.wolfram.com/WedgeProduct.html, but it is still not clear to me how to calculate it. What is the range of wedge product?
For example if I have two vectors in $\mathbb{R}^4$, namely $[1,0,0,0]^{T}$ and $[0,1,0,0]^{T}$, then what is their wedge product?


The wedge product of $e^1$ and $e^2$ is $e^1\wedge e^2$. Cannot be simplified furthermore.

  • $\begingroup$ Just to make things clear for the OP: the wedge product of two vectors is not a vector, but a "2-vector". $\endgroup$
    – mrf
    Feb 25 '13 at 9:40
  • $\begingroup$ So how can I denote the range of wedge product? $\mathbb{R}^n$^$\mathbb{R}^n$? $\endgroup$
    – Sunny88
    Feb 25 '13 at 11:39
  • 1
    $\begingroup$ Usually it is denoted by $\Lambda^2(\mathbb R^n)$ $\endgroup$ Feb 26 '13 at 14:46

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