A091471 - OEIS

%I #14 Sep 27 2023 09:15:38

%S 2,12,464,50224,25095232

%N Number of n X n matrices with entries {-1,1} that are diagonalizable over the complex numbers.

%C See A091472 for definition of diagonalizable and for Mathematica definitions.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DiagonalizableMatrix.html">Diagonalizable Matrix</a>

%H <a href="/index/Mat#binmat">Index entries for sequences related to binary matrices</a>

%t Table[Count[Matrices[n, {-1, 1}], _?DiagonalizableQ], {n, 4}]

%o (Sage)

%o import itertools

%o def a(n):

%o     ans, W = 0, itertools.product([-1, 1], repeat=n*n)

%o     for w in W:

%o         if Matrix(QQbar, n, n, w).is_diagonalizable(): ans += 1

%o     return ans  # _Robin Visser_, Sep 27 2023

%Y Cf. A091470, A091472.

%K nonn,more

%O 1,1

%A _Eric W. Weisstein_, Jan 12 2004

%E a(5) from _Robin Visser_, Sep 27 2023