References
- Smith JS. On the value of a certain arithmetical determinant. Proc. London Math. Soc. 1875/76;7:208–212.
- Haukkanen P, Wang J, Sillanpää J. On Smith’s determinant. Linear Algebra Appl. 1997;258:251–269.
- Korkee I, Haukkanen P. On meet and join matrices associated with incidence functions. Linear Algebra Appl. 2003;372:127–153.
- Sándor J, Crstici B. Handbook of number theory II. Dordrecht: Kluwer Academic Publishers; 2004.
- Wintner A. Diophantine approximations and Hilbert’s space. Am. J. Math. 1944;66:564–578.
- Lindqvist P, Seip K. Note on some greatest common divisor matrices. Acta Arith. 1998;84:149–154.
- Beslin S, Ligh S. Greatest common divisor matrices. Linear Algebra Appl. 1989;118:69–76.
- Bourque K, Ligh S. Matrices associated with arithmetical functions. Linear Multilinear Algebra. 1993;34:261–267.
- Ovall J. An analysis of GCD and LCM matrices via LDLT-factorization. Electron. J. Linear Algebra. 2004;11:51–58.
- Balatoni F. On the eigenvalues of the matrix of the Smith determinant, (Hungarian). Mat. Lapok. 1969;20:397–403.
- Hong S, Loewy R. Asymptotic behavior of eigenvalues of greatest common divisor matrices. Glasgow Math. J. 2004;46:551–569.
- Bhatia R. Infinitely divisible matrices. Am. Math. Monthly. 2006;113:221–235.
- Ilmonen P, Haukkanen P, Merikoski J. On eigenvalues of meet and join matrices associated with incidence functions. Linear Algebra Appl. 2008;429:859–874.
- Cayley A. On the theory of linear transformations. Cambridge Math. J. 1845;4:1–16.
- Gelfand IM, Kapranov MM, Zelevinsky AV. Discriminants, resultants and multidimensional determinants. Boston (MA): Birkhäuser; 1994.
- Qi L. Eigenvalues of a real supersymmetric tensor. J. Symbolic Comput. 2005;40:1302–1324.
- Lim LH. 2005. Singular values and eigenvalues of tensors: a variational approach. Proceedings of the 1st IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP); Puerto Vallarta; p. 129–132.
- Haukkanen P. Higher-dimensional GCD matrices. Linear Algebra Appl. 1992;170:53–63.
- Luque J-G. Hyperdeterminants on semilattices. Linear Multilinear Algebra. 2008;56:333–344.
- Kofidis E, Regalia P. On the best rank-1 approximation of higher-order supersymmetric tensors. SIAM J. Matrix Anal. Appl. 2002;23:863–884.
- Qi L, Teo KL. Multivariate polynomial minimization and its application in signal processing. J. Global Optim. 2003;26:419–433.
- Aigner M. Combinatorial theory. New York (NY): Springer-Verlag; 1986.
- McCarthy P. Introduction to arithmetical functions. New York (NY): Springer-Verlag; 1986.
- Stanley RP. Enumerative combinatorics. Vol. 1. Corrected reprint of the 1986 original. Vol. 49, Cambridge studies in advanced mathematics. Cambridge: Cambridge University Press; 1997.
- Korkee I, Haukkanen P. Bounds for determinants of meet matrices associated with incidence functions. Linear Algebra Appl. 2001;329:77–88.
- Rajarama Bhat BV. On greatest common divisor matrices and their applications. Linear Algebra Appl. 1991;158:77–97.
- Haukkanen P. On meet matrices on posets. Linear Algebra Appl. 1996;249:111–123.