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 …

Eigenvalues and eigenvectors are easy to calculate and the concept is not difficult to understand. I found that there are many applications of eigenvalues and eigenvectors in multivariate analysis.

There are already good answers about importance of eigenvalues / eigenvectors, such as this question and some others, as well as this Wikipedia article. I know the theory and these examples, but n...

May 10, 2015 · Skew-Hermitan matrices are promising for counterexample, since their eigenvalues are purely imaginary. Real skew-Hermitan matrix is just a skew-symmetrical one.

Jul 5, 2015 · A A has no real valued eigenvalues and no real valued eigenvectors. But A A has two complex valued eigenvalues λ1 = i, λ2 = −i λ 1 = i, λ 2 = i and two complex valued eigenvectors. …

I'm studying eigenvector and eigenvalue but there are some confusing things to me. (1) Eigenvectors are not unique (2) If eigenvectors come from distinct eigenvalues, then eigenvectors are unique.

How are the real parts of the eigenvalues of A A related to the (necessarily) real eigenvalues of A +AT A + A T? Answers for complex matrices appreciated as well.

Apr 13, 2017 · Non-square matrices do not have eigenvalues. If the matrix X is a real matrix, the eigenvalues will either be all real, or else there will be complex conjugate pairs.

Jan 26, 2014 · 15 I am confused about the relationship between the invertibility of a matrix and its eigenvalues. What do the eigenvalues of a matrix tell you about whether a matrix is invertible or not? …

Oct 25, 2018 · I got your point. while in that we can modify this question for a 4×4 matrix with A has eigen value 1,1,1,2 . Then can it be possible to have 1,4,3,1/3. this time (det A)^2= (det A^2) satisfied.