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Math Help - Vector product for higher dimensions than 3?

  1. #1
    Senior Member TriKri's Avatar
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    Vector product for higher dimensions than 3?

    I know that the vector product (for \Bbb{R}^3) is defined in a way so that a orthogonal vector is produced from two original vectors. In \Bbb{R}^2 you can't create a vector \neq\overline{0} orthogonal to two linear independent vectors. On the other hand, you can if you only have one vector from the beginning. In \Bbb{R}^4, you can if you have 3 linear independent vectors from the beginning (you'll get a line of possible vectors contrary to if you only have 2 vectors to perform the multiplication with, then you'll get a plane).

    Is there some kind of general vector product for n-1 vectors in \Bbb{R}^n? (this would be almost the same as a method for obtaining a vector orthogonal to the other vectors.)
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    Opalg's Avatar
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    In some ways, the vector product is a feature unique to three-dimensional space. But there is a construction called the wedge product that generalises some of the properties of the vector product to higher-dimensional spaces.
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