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I am trying to solve the following problem. Is there exist a transformation matrix T,different then the block diagonal, with all blocks the same, such that the form of the matrix A=[A1 A2 ; I 0], is preserved? All blocks of A are in R^{nxn}, I is identity and 0 is zero matrix. In other words, is there exist matrix T (again, not block diagonal with all blocks the same) such that T^{-1}*A*T=B, where B=[B1 B2 ; I 0]?

By intuition, such matrix T does not exist, but I do not know how this can be shown.

If anyone has an idea about this please help. Thank you in advance.

Nicolas

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# Block matrix transformation of specific form

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