Ivan Shishkin, Rye (1878)

Problems/Linear algebraExerciseUnreviewed

Determining a Hankel matrix

by Ancient Tree·
18
Difficulty scaleÉchelle de difficulté

This score reflects both the level of the required concepts and the difficulty of the solution.Ce score tient compte à la fois du niveau des notions nécessaires et de la difficulté de la résolution.

  1. 1–10First steps / middle schoolPremiers pas / collège
  2. 11–25Beginner / high schoolDébutant / lycée
  3. 26–50Intermediate / undergraduateIntermédiaire / licence
  4. 51–70Advanced / graduateAvancé / master
  5. 71–90Expert / specializedExpert / spécialisé
  6. 91–100Research levelNiveau recherche
These levels are approximate guides.Ces niveaux sont des repères approximatifs.
·
English
EnglishFrançais
Unreviewed. This problem has not been reviewed by trusted users yet.

How many entries are needed to uniquely determine a m×nm\times n Hankel matrix ?

I solved itMark it doneAdd to my listKeep it in your list
I like this problem1 like

Liked by

Solutions

1
Reveal solutionsAre you sure? Give it a try first.

Solution by Ancient Tree

Discussions0 useful votes

A m×nm\times n Hankel matrix has its entries given by hij=ci+jh_{ij}=c_{i+j} for some sequence ckc_{k}. This means that the terms of the sequence appearing in the matrix are ranging from c2c_{2} to cm+nc_{m+n}, which makes m+n−2+1=m+n−1m+n-2+1=m+n-1 terms.

Report

For an unclear, ambiguous, or possibly incorrect statement, please use the Discussion tab on the right. Report content that needs moderator intervention, such as dangerous, clearly non-mathematical, or plagiarized content.