A 
-matrix is a matrix whose elements
consist only of the numbers 
or 1. For an 
-matrix, the largest possible determinants
(Hadamard's maximum determinant
problem) for 
,
2, ... are 1, 2, 4, 16, 48, 160, ... (OEIS A003433;
Ehrlich and Zeller 1962, Ehrlich 1964), the same as for an 
-matrix. The numbers of distinct 
-matrices having the largest possible determinant are
1, 4, 96, 384, 30720, ... (OEIS A188895).
(-1,1)-Matrix
See also
Hadamard Matrix, Integer MatrixExplore with Wolfram|Alpha
References
Ehrlich, H. "Determinantenabschätzungen für binäre Matrizen." Math. Z. 83, 123-132, 1964.Ehrlich, H. and Zeller, K. "Binäre Matrizen." Z. angew. Math. Mechanik 42, T20-21, 1962.Kahn, J.; Komlós, J.; and Szemeredi, E. "On the Probability that a Random
Matrix is Singular." J. Amer. Math. Soc. 8,
223-240, 1995.Seifter, N. "Upper Bounds for Permanents of 
-Matrices." Israel J. Math. 48,
69-78, 1984.Sloane, N. J. A. Sequences A003433/M1291
and A188895 in "The On-Line Encyclopedia
of Integer Sequences."Wang, E. T.-H. "On Permanents of
-Matrices." Israel J. Math. 18,
353-361, 1974.Referenced on Wolfram|Alpha
(-1,1)-MatrixCite this as:
Weisstein, Eric W. "(-1,1)-Matrix." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/-11-Matrix.html