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Technique Narrative

5-010-MatrixExponential-TechniqueNarrative

Author(s): Kurt Bryan

Keywords: matrix esponential Putzer's Algorithm diagonalization eigenvalues eigenvectors

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Abstract

Resource Image The matrix exponential is a powerful computational and conceptual tool for analyzing systems of linear, constant coefficient, ordinary differential equations (ODE's). This narrative offers a quick introduction to the technique, with examples and exercises

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Article Context

Resource Type
Differential Equation Type
Qualitative Analysis
Application Area
Lesson Length
Technology
Approach
Skills
Key Scientific Process Skills
Assessment Type
Pedagogical Approaches
Vision and Change Core Competencies - Ability
Principles of How People Learn

Description

We include an introduction to Putzer's Algorithm for computing the matrix exponential, a topic not usually covered in introductory ODE courses. This simple algorithm allows one to compute the exponential of any matrix whose eigenvalues are known.

A computer algebra system can be helpful for this material, since the computations can be a bit cumbersome.

For the reader who wants to know a bit more, proofs for many results are included in an appendix.

The analysis, however, relies only on elementary matrix algebra and techniques for series that most students see in a second semester calculus course.

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Authors

Author(s): Kurt Bryan

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