I have several different covariance matrices, and have found the set of eigenvalues for each of them. I noticed that each matrix has one eigenvalue that is zero. This seems like a pattern. Do covariance matrices always have one and only zero-eigenvalue? Why not two? Why not none?
2026-03-30 11:34:48.1774870488
What implications does having a zero eigenvalue in a covariance have?
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In each of your cases, there exists a deterministic linear or affine relation between your variables.
For example this would arise if your variables were "price of X in in the USA in dollars" and "price of X in the USA, expressed in yen", for various commodities X. Or if they were "distance to vacation spot Y in miles" and "distance to vacation spot Y in kilometers", for various places Y. Or, more interestingly, "proportion of students at school Z studying maths ", "proportion of students at school Z studying chemistry", and "proportion of students at school Z studying anything else", for various schools Z.