Web Reference: 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. 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. Sep 4, 2023 · The right eigenvectors are eigenvectors for this transformation, but the left ones for $A^T$, which, geometrically can be totally different. However, the eigenvalues and the dimensions of their corresponding eigenspaces must stay the same.
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