Algebraically, I understand we need to find the normalized eigenvectors to orthogonally diagonalize the matrix to remove the "xy" term. Geometrically, I see that the eigenvectors represent the direction of the conic section's principal axis, therefore finding them we can "rotate" the axis to solve the question. But I can't grasp why the eigenvector is in the direction of the principal axis. Is it just because the eigenvectors in this context are orthogonal? But that still feels "lucky" that they happened to align themselves with the conic section perfectly.
2026-04-04 03:55:42.1775274942
A geometric interpretation of why the principal axis of a conic section is along the Eigenvectors?
103 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in EIGENVALUES-EIGENVECTORS
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