ToeplitzMatrix
gives the n×n Toeplitz matrix with first row and first column being successive integers.
ToeplitzMatrix[{c1,c2,…,cn}]
gives the Toeplitz matrix whose first column consists of elements c1, c2, ….
ToeplitzMatrix[{c1,c2,…,cm},{r1,r2,…, rn}]
gives the Toeplitz matrix with elements ci down the first column, and ri across the first row.
Examples
open allclose allBasic Examples (3)
Scope (5)
Properties & Relations (4)
ToeplitzMatrix[{c1,c2,…}] is Hermitian if c1 is real:
is diagonalizable by a unitary matrix:
ToeplitzMatrix[c,r] is a circulant matrix when r=RotateRight[Reverse[c]]:
The eigenvalues can be found from:
where
is the Fourier matrix and
is DiagonalMatrix[v]:
HankelMatrix and ToeplitzMatrix are related by reversed identity matrix:
Neat Examples (1)
Text
Wolfram Research (2007), ToeplitzMatrix, Wolfram Language function, https://reference.wolfram.com/language/ref/ToeplitzMatrix.html.
CMS
Wolfram Language. 2007. "ToeplitzMatrix." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ToeplitzMatrix.html.
APA
Wolfram Language. (2007). ToeplitzMatrix. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ToeplitzMatrix.html