We now that if we have two EQUIVALENT matrices A,B so: A=SBT where S and T are invertible.
We now that in general there are two bases such that the form SBT is a block matrice divided in four blocks where the one at the top-left is the Identity matrice and the rest is zero. How can I demonstrate that?

Question

We now that if we have two EQUIVALENT matrices A,B so: A=SBT where S and T are invertible.
We now that in general there are two bases such that the form SBT is a block matrice divided in four blocks where the one at the top-left is the Identity matrice and the rest is zero. How can I demonstrate that?

anonymous · Answer

*know

fibonaccichick666 · Answer

I think @eliassaab may be able to help you here

anonymous · Answer

Do you mean similar by saying equivalent?

anonymous · Answer

I saw on wikipedia, I guess I wrote right. (excuse me I'm italian).
 If I've unsderstood A=PBQ A,B are equivalent if P,Q are invertible. If P is the inverse of Q than are similar is it right?
Ps Merry Christmas!!