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UnkleRhaukus

What is the difference between a vector space and a set.

  • one year ago
  • one year ago

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  1. satellite73
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    a raft of axioms that have to be satisfied, as well as a couple of operations

    • one year ago
  2. myko
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    a set in general is just a collection of "objects" with or without any condition imposed on the members of the set. Vector space is also kind of set, but with special condition to be satisfied by the elements that belong to it.

    • one year ago
  3. myko
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    conditions*

    • one year ago
  4. UnkleRhaukus
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    which conditions, axioms, operations, are usually not common to vector spaces and sets

    • one year ago
  5. myko
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    http://en.wikipedia.org/wiki/Vector_space

    • one year ago
  6. UnkleRhaukus
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    is the set of complex numbers a vector space?

    • one year ago
  7. myko
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    yes

    • one year ago
  8. UnkleRhaukus
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    what about the set on n dimensional matrices ?

    • one year ago
  9. UnkleRhaukus
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    n dimensional complex matrices ?

    • one year ago
  10. myko
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    also

    • one year ago
  11. UnkleRhaukus
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    are you sure

    • one year ago
  12. UnkleRhaukus
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    *^ n by n complex matrices ?

    • one year ago
  13. cumin
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    can you add 2 by n complex matrices and get an n by n complex matrix? can you multiply an n by n complex matrix by a scalar (a real number would be a simple scalar to use here maybe) and get an n by n complex matrix as a result? If the answer is yes to both questions, I think that means that n by n complex matrices make up a vector space. If I am wrong I would like to be corrected.

    • one year ago
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