Let a be a matrix of order n over the complex field C It is proved that there exists an invertible matrix P of order n on C such that P ^ - 1AP = R1 A12. A1N 0 a22 .a2n . 0 an2 .ann | Math enthusiast | Mathematical art

Let a be a matrix of order n over the complex field C It is proved that there exists an invertible matrix P of order n on C such that P ^ - 1AP = R1 A12. A1N 0 a22 .a2n . 0 an2 .ann

Let P1 be the eigenvector of a belonging to the eigenvalue R1. Let P1 be a set of bases of C ^ n, P1, P2,..., PN, then p = (P1, P2,..., PN) is reversible and AP = (AP1, ap2,..., APN) = (r1p1, ap2,..., APN) let APJ = ∑ aijpi, j = 2,3,..., n then AP = (P1, P2,..., PN) BB = R1 A12. A1n0 A22. A2

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