منابع مشابه
Divisibilty Properties of Gcd Ve Lcm Matrices
Let a, b and n be positive integers and let S = {x1, x2, . . . , xn} be a set of distinct positive integers. The n × n matrix (Sf ) = (f ((xi, xj))), having f evaluated at the greatest common divisor (xi, xj) of xi and xj as its ij−entry, is called the GCD matrix associated with f on the set S. Similarly, the n × n matrix [Sf ] = (f ([xi, xj ])) is called the LCM matrix associated with f on S. ...
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متن کاملNotes on the divisibility of GCD and LCM Matrices
Let S = {x1,x2, . . . ,xn} be a set of positive integers, and let f be an arithmetical function. The matrices (S) f = [ f (gcd(xi,xj))] and [S] f = [ f (lcm[xi,xj])] are referred to as the greatest common divisor (GCD) and the least common multiple (LCM) matrices on S with respect to f , respectively. In this paper, we assume that the elements of the matrices (S) f and [S] f are integers and st...
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The idea to study infinite matrices whose entries are the coefficients of the powers of a given formal series is rather old and dates back at least to Schur’s posthumous papers on Faber polynomials [39-41]. In 1953, Jabotinsky reconsidered Schur and Shiffer’s [38] work on the subject and developed a systematic study of these matrices [20]. Since then, several applications confirmed that Jabotin...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1992
ISSN: 0024-3795
DOI: 10.1016/0024-3795(92)90409-4