Question

Hadamard Conjecture?

Answer 1

It is a consequence of this definition that the corresponding properties hold for columns as well as rows. The n-dimensional parallelotopespanned by the rows of an n×n Hadamard matrix has the maximum possible n-dimensional volume among parallelotopes spanned by vectors whose entries are bounded in absolute value by 1. Equivalently, a Hadamard matrix has maximal determinantamong matrices with entries of absolute value less than or equal to 1 and so, is an extremal solution of Hadamard's maximal determinant problem.

Certain Hadamard matrices can almost directly be used as an error-correcting codeusing a Hadamard code (generalized in Reed–Muller codes), and are also used in balanced repeated replication (BRR), used by statisticians to estimate the variance of a parameter estimator.