On frame diagonalization of square matrices.

In this paper, we introduce a frame diagonalization of matrices in $ M_n({\mathbb {C}}) $ Mn(C), called QR-frame diagonalization, by using QR-factorization. Furthermore, we show that every matrix <italic>A</italic> in $ M_n({\mathbb {C}}) $ Mn(C) is QR-frame diagonalizable. Also we introduce another frame diagonalization via Hadamard matrices in $ M_n({\mathbb {R}}) $ Mn(R), called Hadamard frame diagonalization, by using Hadamard matrices for <italic>n</italic> = 2, 4 or multiple of 4. We show that every matrix <italic>A</italic> in $ M_n({\mathbb {R}}) $ Mn(R) which <italic>n</italic> = 2, 4 or multiple of 4 is Hadamard frame diagonalizable. In this frame diagonalization, we can find entries on main diagonal Δ by using inner product. Moreover we introduce frame diagonalization of matrices on left quaternionic Hilbert spaces $ M_n({\mathbb {H}}) $ Mn(H). [ABSTRACT FROM AUTHOR]