Student understanding of linear combinations of eigenvectors

Megan Wawro, Kevin Watson, Michelle Zandieh

Research output: Contribution to journalArticle

Abstract

To contribute to the sparse educational research on student understanding of eigenspace, we investigated how students reason about linear combinations of eigenvectors. We present results from student reasoning on two written multiple-choice questions with open-ended justifications involving linear combinations of eigenvectors in which the resultant vector is or is not an eigenvector of the matrix. We detail seven themes that analysis of our data revealed regarding student responses. These themes include: determining if a linear combination of eigenvectors satisfies the equation Ax= λx; reasoning about a linear combination of eigenvectors belonging to a set of eigenvectors; conflating scalars in a linear combination with eigenvalues; thinking eigenvectors must be linearly independent; and reasoning about the number of eigenspace dimensions for a matrix. In the discussion, we explore how themes sometimes cut across questions and how looking across questions gives insight into individuals’ conceptions of eigenspace. Implications for teaching and future research are also offered.

Original languageEnglish (US)
JournalZDM - Mathematics Education
DOIs
StateAccepted/In press - Jan 1 2019

Fingerprint

Eigenvector
Linear Combination
Eigenspace
student
Reasoning
educational research
Justification
Teaching
Linearly
Scalar
Eigenvalue

Keywords

  • Eigenspace
  • Linear algebra
  • Linear combination
  • Student reasoning

ASJC Scopus subject areas

  • Education
  • Mathematics(all)

Cite this

Student understanding of linear combinations of eigenvectors. / Wawro, Megan; Watson, Kevin; Zandieh, Michelle.

In: ZDM - Mathematics Education, 01.01.2019.

Research output: Contribution to journalArticle

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