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In mathematics, the Silverman–Toeplitz theorem, first proved by Otto Toeplitz, is a result in series summability theory characterizing matrix summability methods that are regular. A regular matrix summability method is a linear sequence transformation that preserves the limits of convergent sequences . [ 1 ]
Siegel–Walfisz theorem (analytic number theory) Silverman–Toeplitz theorem (mathematical analysis) Simplicial approximation theorem (algebraic topology) Sinkhorn's theorem (matrix theory) Sion's minimax theorem (game theory) Sipser–Lautemann theorem (probabilistic complexity theory) (structural complexity theory)
Hans Rademacher and Otto Toeplitz, The Enjoyment of Mathematics: Selections from Mathematics for the Amateur (translated by Herbert Zuckerman), Princeton University Press, 1957 [3] [4] Otto Toeplitz, The calculus: a genetic approach, The University of Chicago Press, 2007 ISBN 0-226-80668-5; Toeplitz, Otto (2 July 2018). 2018 pbk edition ...
is called a Toeplitz system if is a Toeplitz matrix. If A {\displaystyle A} is an n × n {\displaystyle n\times n} Toeplitz matrix, then the system has at most only 2 n − 1 {\displaystyle 2n-1} unique values, rather than n 2 {\displaystyle n^{2}} .
Toeplitz algebra, the C*-algebra generated by the unilateral shift on the Hilbert space; Toeplitz Hash Algorithm, used in many network interface controllers; Hellinger–Toeplitz theorem, an everywhere defined symmetric operator on a Hilbert space is bounded; Silverman–Toeplitz theorem, characterizing matrix summability methods which are regular
The inscribed square problem, also known as the square peg problem or the Toeplitz' conjecture, is an unsolved question in geometry: Does every plane simple closed curve contain all four vertices of some square? This is true if the curve is convex or piecewise smooth and in other special cases. The problem was proposed by Otto Toeplitz in 1911. [1]
An circulant matrix takes the form = [] or the transpose of this form (by choice of notation). If each is a square matrix, then the matrix is called a block-circulant matrix.. A circulant matrix is fully specified by one vector, , which appears as the first column (or row) of .
Levinson recursion or Levinson–Durbin recursion is a procedure in linear algebra to recursively calculate the solution to an equation involving a Toeplitz matrix.The algorithm runs in Θ(n 2) time, which is a strong improvement over Gauss–Jordan elimination, which runs in Θ(n 3).
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