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    Determinants and inverses of circulant matrices with Jacobsthal and Jacobsthal-Lucas Numbers
    (ELSEVIER SCIENCE INC, 2012) Bozkurt, Durmus; Tam, Tin-Yau
    Let n >= 3 and let J(n) := circ(J(1),J(2),...,J(n)) and j(n) := circ(j(0),j(1),...,j(n-1)) be the n x n circulant matrices associated with the Jacobsthal numbers J(1),...,J(n) and the Jacobsthal-Lucas numbers j(0),...,j(n-1), respectively. The determinants and the inverses of J(n) and j(n) are obtained in terms of J(1),...,J(n) and j(1),...,j(n-1), respectively. (C) 2012 Elsevier Inc. All rights reserved.
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    Determinants and inverses of r-circulant matrices associated with a number sequence
    (TAYLOR & FRANCIS LTD, 2015) Bozkurt, Durmus; Tam, Tin-Yau
    Let W-n = circ(r) (W-1, W-2, ... , W-n) be the r -circulant matrix associated with the numbers defined by the recursive relation W-n = pW(n-1) + qW(n-2) with initial conditions W-0 = a and W-1 = b, where a, b, p, q is an element of Z and n >= 2. We obtain some formulas for the determinants and inverses of Wn. Some bounds for spectral norms of W-n are obtained as applications.
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    SINGULAR VALUES AND EIGENVALUES OF MATRICES IN so(n)(C) AND sp(n)(C)
    (TUSI MATHEMATICAL RESEARCH GROUP, 2014) Bozkurt, Durmus; Tam, Tin-Yau; Yan, Wen
    We give a complete relation between the singular values and eigenvalues of a complex skew symmetric matrix in terms of multiplicative majorization and double occurrences of singular values and eigenvalues. Similar studies are given for matrices in the algebras sp(n)(C) and sp(n)(R).