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Bounds On The Maximum Determinant For (1,-1) Matrices, C Koukouvinos, M Mitrouli, Jennifer Seberry
Bounds On The Maximum Determinant For (1,-1) Matrices, C Koukouvinos, M Mitrouli, Jennifer Seberry
Professor Jennifer Seberry
We suppose the Hadamard conjecture is true and an Hadamard matrix of order 4t, exists for all t ≥ 1. We use the results for the equivalent SBIBD(4t –1, 2t–1, t–1) to establish the maximum determinant or a lower bound for the maximum determinant for all ±1 matrices. In particular we give numerical results for all orders ≤100.
Values Of Minors Of (1,-1) Incidence Matrices Of Sbibds And Their Application To The Growth Problem, C Koukouvinos, M Mitrouli, Jennifer Seberry
Values Of Minors Of (1,-1) Incidence Matrices Of Sbibds And Their Application To The Growth Problem, C Koukouvinos, M Mitrouli, Jennifer Seberry
Professor Jennifer Seberry
We obtain explicit formulae for the values of the v j minors, j = 0, 1,2 of (1, -1) incidence matrices of SBIBD(v, k, λ). This allows us to obtain explicit information on the growth problem for families of matrices with moderate growth. An open problem remains to establish whether the (1, -1) CP incidence matrices of SBIBD(v, k, λ), can have growth greater than v for families other than Hadamard families.
An Algorithm To Find Formulae And Values Of Minors For Hadamard Matrices, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
An Algorithm To Find Formulae And Values Of Minors For Hadamard Matrices, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
Professor Jennifer Seberry
We give an algorithm to obtain formulae and values for minors of Hadamard matrices. One step in our algorithm allows the (n – j) x (n – j) minors of an Hadamard matrix to be given in terms of the minors of a 2j-1 x 2j-1 matrix. In particular we illustrate our algorithm by finding explicitly all the (n – 4) x (n – 4) minors of an Hadamard matrix.