In linear algebra, a Toeplitz matrix or diagonal-constant matrix, named after Otto Toeplitz, is a matrix in which each descending diagonal from left to right is constant. For instance, the following matrix is a Toeplitz matrix:
Any matrix of the form
is a Toeplitz matrix. If the element of is denoted then we have
In linear algebra, a Toeplitzmatrix or diagonal-constant matrix, named after Otto Toeplitz, is a matrix in which each descending diagonal from left to...
the right relative to the preceding row. It is a particular kind of Toeplitzmatrix. In numerical analysis, circulant matrices are important because they...
block Toeplitzmatrix is another special block matrix, which contains blocks that are repeated down the diagonals of the matrix, as a Toeplitzmatrix has...
n} Hankel matrix, then H = T J n {\displaystyle H=TJ_{n}} where T {\displaystyle T} is an m × n {\displaystyle m\times n} Toeplitzmatrix. If T {\displaystyle...
written as sum of a symmetric and a skew-symmetric matrix. This decomposition is known as the Toeplitz decomposition. Let Mat n {\displaystyle {\mbox{Mat}}_{n}}...
Multiplication operator Tridiagonal matrixToeplitzmatrix Toral Lie algebra Circulant matrix Proof: given the elementary matrix e i j {\displaystyle e_{ij}}...
Look up Toeplitzmatrix in Wiktionary, the free dictionary. Toeplitz or Töplitz may refer to: Töplitz, the German name of Toplița, a city in Romania Toplița...
{\text{ and }}A\mathbf {x} } If M {\displaystyle M} is a symmetric Toeplitzmatrix, i.e. the entries m i j {\displaystyle m_{ij}} are given as a function...
algebra to recursively calculate the solution to an equation involving a Toeplitzmatrix. The algorithm runs in Θ(n2) time, which is a strong improvement over...
of the matrix (one usually deals with square matrices, though all algorithms can be easily generalized to rectangular matrices). Toeplitzmatrix Fay's...
restriction. A bounded operator on H 2 {\displaystyle H^{2}} is Toeplitz if and only if its matrix representation, in the basis { z n , z ∈ C , n ≥ 0 } {\displaystyle...
elements equal or Toeplitz matrices and for the general case as well. In general, the inverse of a tridiagonal matrix is a semiseparable matrix and vice versa...
The Toeplitz Hash Algorithm describes hash functions that compute hash values through matrix multiplication of the key with a suitable Toeplitzmatrix. The...
well. With a complex signal, the matrix to be solved is a Hermitian Toeplitzmatrix, rather than symmetric Toeplitzmatrix. For simplicity, the following...
arbitrary square matrix C can be written as the sum of a Hermitian matrix A and a skew-Hermitian matrix B. This is known as the Toeplitz decomposition of...
matrices used in mathematics, science and engineering. A matrix (plural matrices, or less commonly matrixes) is a rectangular array of numbers called entries...
In applied mathematics, the transfer matrix is a formulation in terms of a block-Toeplitzmatrix of the two-scale equation, which characterizes refinable...
In mathematics, a triangular matrix is a special kind of square matrix. A square matrix is called lower triangular if all the entries above the main diagonal...
persymmetric matrix. A matrix for which the values on each line parallel to the main diagonal are constant is called a Toeplitzmatrix. Centrosymmetric matrix Golub...
correlation Titchmarsh convolution theorem Toeplitzmatrix (convolutions can be considered a Toeplitzmatrix operation where each row is a shifted copy...
the data. However, by formulating the problem as the solution of a Toeplitzmatrix and using Levinson recursion, we can relatively quickly estimate a...
and which represents a symmetric, tridiagonal matrix. For an equidistant grid one gets a Toeplitzmatrix. The 2D case shows all the characteristics of...
M-dependent, and Toeplitz. In exploratory data analysis, the iconography of correlations consists in replacing a correlation matrix by a diagram where...
and has many classical algorithms. Some modern algorithms have used Toeplitzmatrix advances to speed up factor calculations. Let P ( t ) = [ p 11 ( t...
{\displaystyle \mathbf {R} } is a symmetric, p × p {\displaystyle p\times p} Toeplitzmatrix with elements r i j = R ( i − j ) , 0 ≤ i , j < p {\displaystyle r_{ij}=R(i-j)...
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