In this lesson, we learn how to solve first order differential equations with matrices and how to work with an exponential with matrices. By finding the eigenvalues and eigenvectors of the matrix, we can get insight into the behavior of the solution, such as stability and steady states. The real part of the eigenvalues is important for determining stability and the trace of a 2 by 2 stable matrix will be negative.
Differential Equations du/dt = Au and Exponential e^At of a matrix -- Lecture 23. Learn how to solve first order differential equations with matrices and how to work with an exponential with matrices.
Gilbert Strang, 18.06 Linear Algebra, Spring 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 23, 2008). License: Creative Commons BY-NC-SA.
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