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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
Technique
Qualitative Analysis
Application Area
Course
Course Level
Lesson Length
Technology
Approach
Skills
Key Scientific Process Skills
Assessment Type
Pedagogical Approaches
Vision and Change Core Competencies - Ability
Principles of How People Learn
Bloom's Cognitive Level

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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