gives the n×n Hankel matrix with first row and first column being successive integers.
gives the Hankel matrix whose first column consists of entries c1, c2, ….
gives the Hankel matrix with entries ci down the first column, and ri across the last row.
Details and Options
- Hankel matrices typically occur in applications related to approximation theory, functional analysis, numerical analysis and signal processing.
- A Hankel matrix is a matrix that is constant along its antidiagonals. The entries of the Hankel matrix are given by if , and otherwise.
- The entry cm must be the same as r1. »
- For m=n, the Hankel matrix is a symmetric matrix and will have real eigenvalues if the entries ci and rj are all real.
- HankelMatrix[…,TargetStructure->struct] returns the Hankel matrix in the format specified by struct. Possible settings include:
Automatic automatically choose the representation returned "Dense" represent the matrix as a dense matrix "Structured" represent the matrix as a structured array
- With HankelMatrix[…,TargetStructureAutomatic], a dense matrix is returned if the number of matrix entries is less than a preset threshold, and a structured array is returned otherwise.
- For a structured HankelMatrix sa, the following properties "prop" can be accessed as sa["prop"]:
"ColumnVector" vector of entries down the first column "RowVector" vector of entries across the last row "Properties" list of supported properties "Structure" type of structured array "StructuredData" internal data stored by the structured array "StructuredAlgorithms" list of functions with special methods for the structured array "Summary" summary information, represented as a Dataset
- Normal[HankelMatrix[…]] converts the structured Hankel matrix to an ordinary matrix.
Examplesopen allclose all
Basic Examples (3)
HankelMatrix objects include properties that give information about the array:
When appropriate, structured algorithms return another HankelMatrix object:
The transpose is also a HankelMatrix:
Use Prony's method [Wikipedia] to recover the sum of exponentials from the data:
Properties & Relations (6)
Wolfram Research (2007), HankelMatrix, Wolfram Language function, https://reference.wolfram.com/language/ref/HankelMatrix.html (updated 2023).
Wolfram Language. 2007. "HankelMatrix." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2023. https://reference.wolfram.com/language/ref/HankelMatrix.html.
Wolfram Language. (2007). HankelMatrix. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/HankelMatrix.html