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- Regular_Hadamard_matrix abstract "In mathematics a regular Hadamard matrix is a Hadamard matrix whose row and column sums are all equal. While the order of a Hadamard matrix must be 1, 2, or a multiple of 4, regular Hadamard matrices carry the further restriction that the order be a perfect square. The excess, denoted E(H), of a Hadamard matrix H of order n is defined to be the sum of the entries of H. The excess satisfies the bound|E(H)| ≤ n3/2. A Hadamard matrix attains this bound if and only if it is regular.If n = 4u2 is the order of a regular Hadamard matrix, then the excess is ±8u3 and the row and column sums all equal ±2u. It follows that each row has 2u2 ± u positive entries and 2u2 ∓ u negative entries. The orthogonality of rows implies that any two distinct rows have exactly u2 ± u positive entries in common. If H is interpreted as the incidence matrix of a block design, with 1 representing incidence and −1 representing non-incidence, then H corresponds to a symmetric 2-(v,k,λ) design with parameters (4u2, 2u2 ± u, u2 ± u). A design with these parameters is called a Menon design.A number of methods for constructing regular Hadamard matrices are known, and some exhaustive computer searches have been done for regular Hadamard matrices with specified symmetry groups, but it is not known whether every even perfect square is the order of a regular Hadamard matrix. Bush-type Hadamard matrices are regular Hadamard matrices of a special form, and are connected with finite projective planes.Like Hadamard matrices more generally, regular Hadamard matrices are named after Jacques Hadamard. Menon designs are named after P Kesava Menon, and Bush-type Hadamard matrices are named after Kenneth A. Bush.".
- Regular_Hadamard_matrix wikiPageID "11338044".
- Regular_Hadamard_matrix wikiPageLength "2477".
- Regular_Hadamard_matrix wikiPageOutDegree "12".
- Regular_Hadamard_matrix wikiPageRevisionID "607163471".
- Regular_Hadamard_matrix wikiPageWikiLink Block_design.
- Regular_Hadamard_matrix wikiPageWikiLink Category:Matrices.
- Regular_Hadamard_matrix wikiPageWikiLink Charles_Colbourn.
- Regular_Hadamard_matrix wikiPageWikiLink Hadamard_matrix.
- Regular_Hadamard_matrix wikiPageWikiLink Incidence_matrix.
- Regular_Hadamard_matrix wikiPageWikiLink Jacques_Hadamard.
- Regular_Hadamard_matrix wikiPageWikiLink Jeff_Dinitz.
- Regular_Hadamard_matrix wikiPageWikiLink Jennifer_Seberry.
- Regular_Hadamard_matrix wikiPageWikiLink Mathematics.
- Regular_Hadamard_matrix wikiPageWikiLink P_Kesava_Menon.
- Regular_Hadamard_matrix wikiPageWikiLink Perfect_square.
- Regular_Hadamard_matrix wikiPageWikiLink Projective_plane.
- Regular_Hadamard_matrix wikiPageWikiLinkText "Menon design".
- Regular_Hadamard_matrix wikiPageWikiLinkText "Menon designs".
- Regular_Hadamard_matrix wikiPageWikiLinkText "Regular Hadamard matrix".
- Regular_Hadamard_matrix hasPhotoCollection Regular_Hadamard_matrix.
- Regular_Hadamard_matrix wikiPageUsesTemplate Template:Combin-stub.
- Regular_Hadamard_matrix subject Category:Matrices.
- Regular_Hadamard_matrix hypernym Matrix.
- Regular_Hadamard_matrix type AnatomicalStructure.
- Regular_Hadamard_matrix type Combinatoric.
- Regular_Hadamard_matrix type Matrix.
- Regular_Hadamard_matrix comment "In mathematics a regular Hadamard matrix is a Hadamard matrix whose row and column sums are all equal. While the order of a Hadamard matrix must be 1, 2, or a multiple of 4, regular Hadamard matrices carry the further restriction that the order be a perfect square. The excess, denoted E(H), of a Hadamard matrix H of order n is defined to be the sum of the entries of H. The excess satisfies the bound|E(H)| ≤ n3/2.".
- Regular_Hadamard_matrix label "Regular Hadamard matrix".
- Regular_Hadamard_matrix sameAs m.02r85g0.
- Regular_Hadamard_matrix sameAs Q7309581.
- Regular_Hadamard_matrix sameAs Q7309581.
- Regular_Hadamard_matrix wasDerivedFrom Regular_Hadamard_matrix?oldid=607163471.
- Regular_Hadamard_matrix isPrimaryTopicOf Regular_Hadamard_matrix.