Difference between revisions of "Manuals/calci/HANKEL"

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(Created page with "<div style="font-size:30px">'''HANKEL'''</div><br/>")
 
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<div style="font-size:30px">'''HANKEL'''</div><br/>
 
<div style="font-size:30px">'''HANKEL'''</div><br/>
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<div style="font-size:30px">'''MATRIX("HANKEL",order)'''</div><br/>
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*<math>order</math> is the order of the  hankel matrix.
 +
 +
==Description==
 +
*This function gives the matrix with the property of hankel matrix.
 +
*A hankel matrix is a square matrix with constant skew diagonals.
 +
*If the i,j element of Hankel matrix A is denoted <math>A_{i,j}</math>, then we have
 +
<math>A_{i,j} = A_{i-1,j+1}</math>.
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*i.e., The form of Hankel matrix is:
 +
<math>\begin{bmatrix}
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a & b & c & d & e \\
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b & c & d & e & f \\
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c & d & e & f & g \\
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d & e & f & g & h \\
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e & f & g & h & i \\
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\end{bmatrix}</math>.
 +
*A hankel matrix is  also called as catalecticant matrix.
 +
*Here MATRIX("hankel") is gives the hankel matrix of order 3 with decimal values.
 +
*A Hankel matrix is an upside-down Toeplitz matrix.
 +
*A matrix whose entries along a parallel to the main anti-diagonal are equal, for each parallel.
 +
*Equivalently, is a Hankel matrix if and only if there exists a sequence, such that ,If are square matrices, then  is referred to as a block Hankel matrix.
 +
 +
==Examples==
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#MATRIX("hankel")
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{| class="wikitable"
 +
|-
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| 0.6414852568414062 || 0.9679132911842316 || 0.6076015164144337
 +
|-
 +
| 0.9679132911842316 || 0.6076015164144337 || 0.6414852568414062
 +
|-
 +
| 0.6076015164144337 || 0.6414852568414062 || 0.9679132911842316
 +
|}

Revision as of 10:01, 24 April 2015

HANKEL


MATRIX("HANKEL",order)


  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle order} is the order of the hankel matrix.

Description

  • This function gives the matrix with the property of hankel matrix.
  • A hankel matrix is a square matrix with constant skew diagonals.
  • If the i,j element of Hankel matrix A is denoted Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A_{i,j}} , then we have

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A_{i,j} = A_{i-1,j+1}} .

  • i.e., The form of Hankel matrix is:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{bmatrix} a & b & c & d & e \\ b & c & d & e & f \\ c & d & e & f & g \\ d & e & f & g & h \\ e & f & g & h & i \\ \end{bmatrix}} .

  • A hankel matrix is also called as catalecticant matrix.
  • Here MATRIX("hankel") is gives the hankel matrix of order 3 with decimal values.
  • A Hankel matrix is an upside-down Toeplitz matrix.
  • A matrix whose entries along a parallel to the main anti-diagonal are equal, for each parallel.
  • Equivalently, is a Hankel matrix if and only if there exists a sequence, such that ,If are square matrices, then is referred to as a block Hankel matrix.

Examples

  1. MATRIX("hankel")
0.6414852568414062 0.9679132911842316 0.6076015164144337
0.9679132911842316 0.6076015164144337 0.6414852568414062
0.6076015164144337 0.6414852568414062 0.9679132911842316
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