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Matrix rank properties

Posted on: July 28th, 2013 by
1

Let A and B be any two matrices. Show that
rank(A+B) <= rank(A)+rank(B)
rank(AB) <= min{rank(A), rank(B)}


One Response to Matrix rank properties

  1. Mathav had this to say about that:

    Row space of A+B is a subset of Row space of A + Row space of B. That shows rank(A+B) <= rank(A)+rank(B)
    Column space of AB is a subset of Column space of A. Hence rank(AB) <=rank A
    Row space of AB is a subset of Row space of B
    rank(AB) <= rank(B)


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