**block form**[E2,GK]: Let M=R^{T}R 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.**Hadamard conjecture**[P]: the conjecture that a Hadamard matrix exists for every allowed order.**Hadamard matrix**[Had]: a matrix with entries {-1, +1} such that rows are pairwise orthogonal. The order of a Hadamard matrix must be 1, 2 or 4n with n an integer.**Kronecker product:**If A is a p×q matrix and B is an r×s matrix, then the Kronecker product, A⊗B, is the pr×qs matrixa(1,1)B a(1,2)B ... a(1,q)B . . . . . . . a(p,1)B a(p,2)B ... a(p,q)B

where a(i,j) is the element of A in row i and column j. (Also known as the tensor product.)**Sylvester 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 S_{0}be the 1 × 1 (Hadamard) matrix (1). A Hadamard matrix, S_{n}, of order 2^{n}, is obtained by applying the Sylvester construction, S_{n}=H_{2}⊗ S_{n-1}, where H_{2}is the Hadamard matrix of order 2:1 1 1 -1.

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Page created 26 January 2002.

Last modified 18 June 2003.

Comments: maxdet@indiana.edu