A091471 Number of n X n matrices with entries {-1,1} that are diagonalizable over the complex numbers.

2, 12, 464, 50224, 25095232

Offset: 1

Author

Eric W. Weisstein, Jan 12 2004

Keywords

• nonn
• more

Comments

See A091472 for definition of diagonalizable and for Mathematica definitions.

Links

• Eric Weisstein's World of Mathematics, Diagonalizable Matrix
• Index entries for sequences related to binary matrices

Crossrefs

Cf. A091470, A091472.

Programs

Mathematica

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

Sage

import itertools
def a(n):
    ans, W = 0, itertools.product([-1, 1], repeat=n*n)
    for w in W:
        if Matrix(QQbar, n, n, w).is_diagonalizable(): ans += 1
    return ans  # Robin Visser, Sep 27 2023

Extensions

a(5) from Robin Visser, Sep 27 2023