Glossary of terms for the maximal determinant problem
block form[E2,GK]: Let M=RTR be an n×n
matrix. A block of size r is an r×r matrix with diagonal elements n
and all other elements 3. M is of block form if it consists of such blocks
along the diagonal and elements -1 elsewhere.
equivalence of matrices: Two
matrices are equivalent when one can be obtained from the other
by a series of permutations and negations of rows and columns.
excess: The excess of a Hadamard
matrix is the sum of its elements.
where a(i,j) is the element of A in row i and column j. (Also known as
the tensor product.)
construction[Sy]: If A and B are
Hadamard matrices of orders p and q, then a Hadamard matrix of order pq is
formed by taking the Kronecker product A ⊗ B.
Sylvester matrix[Sy]: Let S0 be the
1 × 1 (Hadamard) matrix (1). A Hadamard matrix, Sn, of order
2n, is obtained by applying the Sylvester construction,
Sn=H2 ⊗ Sn-1,
where H2 is the Hadamard matrix of order 2: