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How to extend?

  1. Mar 21, 2006 #1
    Questions from Abbas Edalat's notes
    http://www.doc.ic.ac.uk/~ae/teaching.html#quantum

    It's about vector space, linear independence and linear dependence of vectors or something else.

    Thanks!

    Generalize the following notions and properties given for the vector space C^2 in the notes to C^d.
    1) Define the norm \omega of a vector and the inner product of two vectors \omega(1) and \omega(2) in C^d. What is the dual of a vector \omega in C^d and what can it be identified with?

    2) Define linear independence and linear dependence of vectors in C^d.

    3) What is the least integer n such that any set of n vectors in C^d will be linearly dependent?

    4) What is a basis of C^d? How many linearly independent vectors it takes to get a basis for C^d?

    5) Define the notion of an orthonormal basis for C^d. What would be the standard basis of C^d?
     
    Last edited by a moderator: Mar 21, 2006
  2. jcsd
  3. Mar 21, 2006 #2

    HallsofIvy

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    What have you tried? What are the definitions of those things in C^3?
     
  4. Mar 21, 2006 #3
    I'm sorry, but I really want to say is as the file bellow. Thanks again.
     

    Attached Files:

  5. Mar 22, 2006 #4

    HallsofIvy

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    1. Many people will not download a "Word" document from someone they do not know.

    2. I did go ahead and look at it, against my better judgement, and it adds nothing- it's just a statement of the problems. You have not responded to any of my questions: What have you tried? What are the definitions of those things in C^2?
     
  6. Mar 22, 2006 #5
    Thanks anyway, HallsofIvy. I think I can do that now.
    What I define the C^2, C^d, R^2, and D^d have the meaning that C^2 is a 2-dimension complex Hilbert space, and C^d a d-dimension complex Hilbert space; similarly,R^2 is a 2-dimension real space, and R^d a d-dimension real number space.And the norm \omega is the norm of omega.
     
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