Web Reference: There is no rotation. These favored vectors are precisely the eigenvectors and the amount by which each of these favored vectors stretches or compresses is the eigenvalue. So why are these eigenvectors and eigenvalues important? Consider the eigenvector corresponding to the maximum (absolute) eigenvalue. Feb 23, 2011 · 9 Eigenvalues and eigenvectors are central to the definition of measurement in quantum mechanics Measurements are what you do during experiments, so this is obviously of central importance to a Physics subject. The state of a system is a vector in Hilbert space, an infinite dimensional space square integrable functions. May 8, 2012 · 81 In general, for any matrix, the eigenvectors are NOT always orthogonal. But for a special type of matrix, symmetric matrix, the eigenvalues are always real and eigenvectors corresponding to distinct eigenvalues are always orthogonal. If the eigenvalues are not distinct, an orthogonal basis for this eigenspace can be chosen using Gram-Schmidt.
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