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Linear Independence of Vectors over C

  1. Jan 30, 2010 #1

    I just want to confirm something. I have [tex]A,B\in M_{nm}(\mathbb{C})[/tex] and I want to prove they are linearly independent. Since they are over the complex field, do I have to prove:

    [tex](a_1+ib_1)A+(a_2+ib_2)B=0 \ \Leftrightarrow \ a_1=a_2=b_1=b_2=0[/tex] ?

  2. jcsd
  3. Jan 30, 2010 #2
    Yes this is what you want to show
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