Similar matricies

  1. daniel_i_l

    daniel_i_l 866
    Gold Member

    1. The problem statement, all variables and given/known data
    Prove or disprove the following statement:
    If A is a singular matrix (detA=0) the it's similar to a matrix with a row of zeros.


    2. Relevant equations



    3. The attempt at a solution
    I know that A has an e-value 0 which means that it's similar to a matrix that has a column of zeros but how do I relate that to the rows?
    Thanks.
     
  2. jcsd
  3. mjsd

    mjsd 860
    Homework Helper

    ok, note that det (M) = product of eigenvalues of M
     
  4. matt grime

    matt grime 9,395
    Science Advisor
    Homework Helper

    Since det(A)=0, there is a row relation.

    Or, consider what you do know. A^t has det 0, so there is an M with

    (MA^tM^-1)

    a matrix with a column of zeroes.

    Now how do we get A back out again?
     
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