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?
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Sunny88
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The wedge product of $e^1$ and $e^2$ is $e^1\wedge e^2$. Cannot be simplified furthermore.
Emanuele Paolini
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Just to make things clear for the OP: the wedge product of two vectors is not a vector, but a "2-vector". – mrf Feb 25 '13 at 09:40
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So how can I denote the range of wedge product? $\mathbb{R}^n$^$\mathbb{R}^n$? – Sunny88 Feb 25 '13 at 11:39
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1Usually it is denoted by $\Lambda^2(\mathbb R^n)$ – Emanuele Paolini Feb 26 '13 at 14:46