Visualizing the inner product space ℝ^m×n in a MATLAB-assisted linear algebra classroom

ABSTRACT

This linear algebra note offers teaching and learning ideas in the treatment of the inner product space ${\mathbb{R}}^{m\times n}$ in a technology-supported learning environment. Classroom activities proposed in this note demonstrate creative ways of integrating MATLAB technology into various properties of Frobenius inner product as visualization tools that complement the algebraic approach. As implemented in linear algebra lessons in a university in the Unites States, the article also incorporates algebraic and visual work of students who experienced these activities with MATLAB software. The connection between the Frobenius norm and the Euclidean norm is also emphasized.

KEYWORDS:

• linear algebra
• inner product space
• Frobenius norm
• technology-assisted learning
• MATLAB
• vector space of m × n matrices

Acknowledgments

I would like to thank the International Journal of Mathematical Education in Science and Technology editors and anonymous reviewers for their helpful comments and suggestions on earlier drafts.

Disclosure statement

No potential conflict of interest was reported by the author.