From the course: Complete Guide to Differential Equations Foundations for Data Science

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Complex eigenvalues

Complex eigenvalues

From the course: Complete Guide to Differential Equations Foundations for Data Science

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Complex eigenvalues

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- [Instructor] In the previous video, you worked with real distinct eigenvalues. But what do you do if you end up obtaining eigenvalues that are not real? Let's review how you obtain complex eigenvalues, and how to solve them. When solving a linear homogenous system of first order differential equations, you can use the matrix method where you gather eigenvalues by ensuring the determinant of the matrix is zero. Once you solve this determinant, one option is you can have complex eigenvalues. Note that you can use the quadratic formula when solving for your eigenvalues where you have lambda equals negative B, plus or minus the square root of these squared, minus four, multiplied by A, multiplied by C, divide all that by two, multiplied by A. This formula will be more heavily used in this video compared to the other two eigenvalue videos, just because it is very common to do that with complex eigenvalues. So for example, if you're solving a two by two matrix, then you'll have two…

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