Feb 23, 2011 · 8 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.

Edit: If $A$ has $n$ distinct eigenvalues then $A$ is diagonalizable (because it has a basis of eigenvalues). Two diagonal matrices with the same eigenvalues are similar and so $A$ and $B$ are …

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...

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.

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.

It is true that the eigenvalues (counting multiplicity) of $AB$ are the same as those of $BA$. This is a corollary of Theorem 1.3.22 in the second edition of "Matrix Analysis" by Horn and Johnson, which is …

I am trying to prove some statements about singular value decomposition, but I am not sure what the difference between singular value and eigenvalue is. Is "singular value" just another name for

Mar 12, 2016 · Now compute the frequencies as eigenvalues and normal modes of oscillation as eigenvectors. Notice that the eigenvalue $0$, corresponding to uniform motion of the system as a …

Apr 27, 2018 · I know that you can find the eigenvalues by finding the $\det (A-\lambda \cdot I)$, but it seems to me that the computation will be rather difficult to compute as it is a $4 \times 4$ matrix.