Intro to Eigenvalues/Eigenvectors:    • Using determinants to compute eigenva...  
Intro to Diagonalization:    • How the Diagonalization Process Works  
REAL Diagonalization Example:    • Full Example: Diagonalizing a Matrix  
Why Diagonal Matrices are Awesome:    • Diagonal Matrices are Freaking Awesome  
Full Linear Algebra Playlist:    • Linear Algebra (Full Course)  

In this video we will see an example of compute eigenvalues, eigenvectors and ultimately diagonalizing a matrix when the eigenvalues are complex or imaginary numbers. We begin by setting up the eigenvalue/eigenvector formula. For a 2x2 matrix, this becomes a quadratic equation and indeed this can have complex solutions. Row reductions, gaussian elimination, row echelon form all work the exact same way to compute the eigenvectors but now we can multiply by complex numbers as well.

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YOUR TURN! Learning math requires more than just watching videos, so make sure you reflect, ask questions, and do lots of practice problems!
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►Full Multivariable Calculus Playlist:    • Calculus III: Multivariable Calculus ...  

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Other Course Playlists:

►CALCULUS I:    • Calculus I (Limits, Derivative, Integ...  

► CALCULUS II:    • Calculus II (Integration Methods, Ser...  

►DISCRETE MATH:    • Discrete Math (Full Course: Sets, Log...  

►LINEAR ALGEBRA:    • Linear Algebra (Full Course)  

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   • Cool Math Series  

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This video was created by Dr. Trefor Bazett. I'm an Assistant Teaching Professor at the University of Victoria.

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