Tag · 2 problems · 2 fields

Open problems tagged matrices

2 problems in the Math Lab index touch matrices, spanning Number Theory, Geometry & Packing. Each carries a precise statement, an honest status, and a computational line of attack.

Hadamard conjectureNumber Theoryuntouched

A Hadamard matrix — a ±1 matrix with pairwise orthogonal rows — exists for every order divisible by 4.

Hadamard's maximal determinant problemGeometry & Packinguntouched

What is the largest possible determinant of an n×n matrix with entries ±1? Hadamard's bound n^(n/2) is attained only at Hadamard orders; other orders are subtler.