# Continuation: Repeated Real Eigenvalues, Complex Eigenvalues

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Lesson Summary:

In this lecture, we learn about solving systems using matrix algebra. We are reminded to find the characteristic equation, calculate its eigenvalues and eigenvectors, and use them to form a general solution. The lecture then delves into the more complicated cases of repeated real eigenvalues and complex eigenvalues. The lecturer goes through an example of a circular fish tank to demonstrate how to set up the differential equations and find the characteristic equation. The characteristic equation in this case turns out to have a repeated real eigenvalue of -3 and a solution to this problem requires a different approach.

Lesson Description:

Continuation: Repeated Real Eigenvalues, Complex Eigenvalues -- Lecture 26. Learn more about solving systems using Matrix Algebra.

Arthur Mattuck, 18.03 Differential Equations, Spring 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 27, 2008). License: Creative Commons BY-NC-SA.