Equivalent Matrices: Definition & A=B

iVenky
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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.
 
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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 A= B^{-1}CB as well as C= BAB^{-1}. 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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