HankelMatrix

HankelMatrix[n]

gives the n×n Hankel matrix with first row and first column being successive integers.

HankelMatrix[{c1,c2,…,cn}]

gives the Hankel matrix whose first column consists of elements c1, c2, ….

HankelMatrix[{c1,c2,…,cm},{r1,r2,…, rn}]

gives the Hankel matrix with elements ci down the first column, and ri across the last row.

Details

  • The element cm must be the same as r1. »

Examples

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Basic Examples  (3)

4×4 Hankel matrix:

Scope  (4)

Make a Hankel matrix of machine numbers:

Make a Hankel matrix with 24-digit precision:

Complex entries:

Non-square Hankel matrices:

Properties & Relations  (5)

Size-20 Hankel matrix:

The determinant of the Hankel matrix of size is :

A square Hankel matrix with real entries is symmetric:

HankelMatrix[c,RotateRight[c]] is a square anticirculant matrix:

Square anticirculant matrices have eigenvector {1,…} with eigenvalue c1+c2+…:

HankelMatrix and ToeplitzMatrix are related by a reversed identity matrix:

Possible Issues  (1)

If element cm is not the same as r1, cm is used and r1 is ignored:

Neat Examples  (1)

Wolfram Research (2007), HankelMatrix, Wolfram Language function, https://reference.wolfram.com/language/ref/HankelMatrix.html.

Text

Wolfram Research (2007), HankelMatrix, Wolfram Language function, https://reference.wolfram.com/language/ref/HankelMatrix.html.

CMS

Wolfram Language. 2007. "HankelMatrix." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/HankelMatrix.html.

APA

Wolfram Language. (2007). HankelMatrix. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/HankelMatrix.html

BibTeX

@misc{reference.wolfram_2022_hankelmatrix, author="Wolfram Research", title="{HankelMatrix}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/HankelMatrix.html}", note=[Accessed: 05-June-2023 ]}

BibLaTeX

@online{reference.wolfram_2022_hankelmatrix, organization={Wolfram Research}, title={HankelMatrix}, year={2007}, url={https://reference.wolfram.com/language/ref/HankelMatrix.html}, note=[Accessed: 05-June-2023 ]}