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 …

Apr 19, 2021 · The fastest way to compute the eigenvalues in this case is to recognize that this matrix is a rank 1 update of a multiple of the identity matrix.

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...

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.

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

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 …

Feb 19, 2017 · How are the eigenvalues of $A$ and $AA^T$ related? What I have come up with so far is that if we let $\lambda_1,\ldots,\lambda_n$ denote the eigenvalues of $A$,

Jul 5, 2015 · 1) If a matrix has 1 eigenvalue as zero, the dimension of its kernel may be 1 or more (depends upon the number of other eigenvalues). 2) If it has n distinct eigenvalues its rank is atleast n.