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What is an Eigenvector? Eigenvalue?

To watch this video with a voice-over audio explanation, click here    • What is an Eigenvector? Eigenvalue? (...   This animation, created using MATLAB, illustrates how eigenvectors are vectors for which matrix multiplication is identical to scalar multiplication. Eigenvectors are special in that not every vector exhibits this property (shown by the first 3 vectors in this video). If the property A*u = lambda*u, then we see that the preimage, u, is an eigenvector with corresponding eigenvalue, lambda, since its image, A*u is merely a scalar multiple of u itself, namely lambda*u. The first preimage in this video is the unit circle (red); its image is the distorted-looking ellipse (blue). Any shape can illustrate the eigenvectors which is why the "STOP" sign is used afterward. Note that this video is primarily useful for the CONCEPT of eigenvectors/eigenvalues. For additional help with "how to find" eigenvectors/eigenvalues, consider some supplemental aid.