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Need help: Proof Null-rank theorem with block matrices

  1. Jun 6, 2008 #1
    hi to all : ))
    (excuse me for my english ^^')

    I need help and I hope you can give me an hand, i must proof the null-rank theorem using block matrices but i can't resolve it.
    This are the information in my possession:

    I have the a function

    f: R^n --->R^m
    x --->y=Ax

    I must reorder columns of the matrix A (m*n) and write A as:

    (A1 A2)
    (A3 A4)

    where:
    A1 is (r*r) with rankA=r
    A2 is (r*q) with q=n-r
    A3 is (p*r) with p=m-r
    A4 is (p*q)

    then resolving this linear sistem:

    (A1 A2) (x1) = (c)
    (A3 A4) (x2) (d)

    I would find a proof for the null rank theorem.

    Can someone help me pls? thk : ))
     
  2. jcsd
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