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QBobWatson / gt-linalg

Interactive Linear Algebra, free online textbook at Georgia Tech
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Feedback on complex-eigenvalues #333

Open rstrauss-logyx opened 4 years ago

rstrauss-logyx commented 4 years ago

In reference to version 224734d7be7ff0c4a8adb3a206356ea122112f33 a.k.a. https://textbooks.math.gatech.edu/ila/complex-eigenvalues.html The 3x3 example is wrong. The eigenvalues are correct, but the last 2 "We can verify" statements is wrong. The product of the first 2 is the middle matrix, but that's not the right product. This is easily seen in the 3rd (bottom) term. Maybe you just matched the eigenvalue 2 with eigenvector 3... At the same time, MatLab gives eigenvector 2 as -0.3660 - 0.2745i -0.2745 + 0.3660i 0.7625 + 0.0000i Why is MatLab's eigenvector about 1/32 as large? Does this factor matter?

kaymachi commented 3 years ago

As long as the two results (for the second eigenvector) are a scalar multiple of each other, it's alright. There's infinitely many eigenvectors for any given eigenvalue. Their union is the corresponding eigenspace.

rstrauss-logyx commented 3 years ago

Still, the "we can verify" statements are wrong. The first statement should have the 4-3i/5 (not the 4+3i/5) and the second should have the 4+3i/5...