Rank of matrix

  • Thread starter bernoli123
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  • #1
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check that, for any nxn matrices A,B then rank(AB) (> or =) rank A +rank(B)-n
 

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  • #2
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Are you familiar with the Rank-Nullity Theorem?
 
  • #3
HallsofIvy
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Suppose B:U-> V and A:V->W. The rank of B is the dimension of B(U) in V, the rank of A is the dimension of A(V)->W, and the rank of AB is the dimension of AB(U) in W. In order that z be in AB(U), it must be in A(V) so that z= A(y) for some y in U. And y must be in B(U) so that y= Bx for some x in U.
 

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