|
%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
| 