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Redheffer matrix information


In mathematics, a Redheffer matrix, often denoted as studied by Redheffer (1977), is a square (0,1) matrix whose entries aij are 1 if i divides j or if j = 1; otherwise, aij = 0. It is useful in some contexts to express Dirichlet convolution, or convolved divisors sums, in terms of matrix products involving the transpose of the Redheffer matrix.

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Redheffer matrix

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In mathematics, a Redheffer matrix, often denoted A n {\displaystyle A_{n}} as studied by Redheffer (1977), is a square (0,1) matrix whose entries aij...

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List of named matrices

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matrices used in mathematics, science and engineering. A matrix (plural matrices, or less commonly matrixes) is a rectangular array of numbers called entries...

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Logical matrix

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matrix, binary matrix, relation matrix, Boolean matrix, or (0, 1)-matrix is a matrix with entries from the Boolean domain B = {0, 1}. Such a matrix can...

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Redheffer star product

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matrices from different linear scatterers, the Redheffer star product yields the combined scattering matrix produced when some or all of the output channels...

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Raymond Redheffer

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calculus in his book with Sokolnikoff. He is known for the Redheffer matrix, the Redheffer star product, and for (with Charles Eames) his 1966 timeline...

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Riemann hypothesis

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paragraph 14.25 in Titchmarsh (1986)). The determinant of the order n Redheffer matrix is equal to M(n), so the Riemann hypothesis can also be stated as a...

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Mertens function

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Franel–Landau theorem. M(n) is the determinant of the n × n Redheffer matrix, a (0, 1) matrix in which aij is 1 if either j is 1 or i divides j. M ( x )...

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Linear fractional transformation

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with the Redheffer star product allows them to be applied to the scattering theory of general differential equations, including the S-matrix approach...

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Early history of video games

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from the original on 2015-12-22. Retrieved 2014-11-16. Varley, p. 119 Redheffer, Raymond (1948). "A Machine for Playing the Game Nim". American Mathematical...

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