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Equivalent matrices

  1. Oct 14, 2012 #1
    What is the exact definition for equivalent matrices?

    Is it necessary that it should be A = B if A,B are two matrices?

    Thanks a lot.
     
  2. jcsd
  3. Oct 14, 2012 #2

    HallsofIvy

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    The standard definition of "equivalent" for matrices (in any Linear Algebra text) is
    "Matrices A and C are equivalent if and only if there exist an invertible matrix, B, such that BA= CB." Since B is invertible, that is the same as saying that [itex]A= B^{-1}CB[/itex] as well as [itex]C= BAB^{-1}[/itex]. From a more abstract point of view, matrices A and C are equivalent if and only if they represent the same linear transformation, on some vector spaces, as represented in different bases.
     
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