# [Article] On the Structure of Finite Continuous Groups with by Zeldin S. D.

By Zeldin S. D.

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The most general transformation V which connects the involutional matrices A and B of the lemma via a similarity transformation V À1 AV B is given by V FA Y YFB (2X1X6) where FA and FB are the same function of A and B, respectively. 1 Involutional transformations 19 Remark. If both A and B are IUH matrices, then so is Y ; however, V is unitary but not involutional in general, for V 2 AB. In two dimensions, the involutional matrices A, B and Y are all improper whereas V is proper, being a product of two improper matrices.

1. The most general transformation V which connects the involutional matrices A and B of the lemma via a similarity transformation V À1 AV B is given by V FA Y YFB (2X1X6) where FA and FB are the same function of A and B, respectively. 1 Involutional transformations 19 Remark. If both A and B are IUH matrices, then so is Y ; however, V is unitary but not involutional in general, for V 2 AB. In two dimensions, the involutional matrices A, B and Y are all improper whereas V is proper, being a product of two improper matrices.

E. AB BA 2c1, c T À1 then there exists an involutional transformation that interchanges A and B via YAY B or A YBY ; Y2 1 (2X1X4) where Y (A B)a(2 2c)1a2 (2X1X5) The proof is elementary. 4). 1. The most general transformation V which connects the involutional matrices A and B of the lemma via a similarity transformation V À1 AV B is given by V FA Y YFB (2X1X6) where FA and FB are the same function of A and B, respectively. 1 Involutional transformations 19 Remark. If both A and B are IUH matrices, then so is Y ; however, V is unitary but not involutional in general, for V 2 AB.