SHADOW MATRICES



© Nickolay Balonin, 5.01.2015


Shadow matrices S alow construct two circulant cores of Jacobsthal matrices Q: the latest are cores of two border two circulant C-matrices. They can consist of symmetric circulant A-block and B-block based on secuence [b;–Rb], R – reversed identity matrix.




Meander of Hadamard Family Matrices




Shadow matrices noted by symbol "e": it is "younger family" of Euler matrices for orders n=4k ! Two-circulant three level (a,–b,d)-matrices constructed via conference matrices and their orthogonalised cores: a=1, b=1–2*d, d=(sqrt(2*n+1)–3)/(n–4) –diagonal entry (for n=4, d=b=1).

On Line Procedure



Shadow matrices Family

Euler matrices E alow construct two circulant cores of Jacobsthal matrices Q: the latest are cores of two border two circulant H-matrices. They can consist of the set of symmetric, asymmetric and skew circulant A, B-blocks.

СЛОЖНОСОСТАВНАЯ МАТРИЦА 44

CRETAN MATRICES

a=1, b=1–2*d, d=(sqrt(2*n+1)–1)/n – diagonal entry



Conference matrix C6



Ortagonalised core S5 and shadow matrix e4



Conference matrix C10



Ortagonalised core S9 and shadow matrix e8 following S9



Conference matrix C14



Ortagonalised core S13 and shadow matrix e12


СВЯЗЬ С КОНФЕРЕНЦ-МАТРИЦАМИ (ЯДРА)



Conference matrix C6



Ortagonalised core S5 and shadow matrix e4=H4



Conference matrix C10



Ortagonalised core S9 and shadow matrix e8



Conference matrix C14



Ortagonalised core S13 and shadow matrix e12



Conference matrix C18



Ortagonalised core S17 and shadow matrix e16





EULER MATRICES CATALOGUE | | MERSENNE MATRICES CATALOGUE



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