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- How to intuitively understand eigenvalue and eigenvector?
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
- Are matrices with the same eigenvalues always similar?
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 similar
- Real life examples for eigenvalues eigenvectors
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
- All tricks to find eigenvalues in $3\times 3$ in a faster way?
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
- Do non-square matrices have eigenvalues? - Mathematics Stack Exchange
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
- What are the Eigenvalues of $A^2?$ - Mathematics Stack Exchange
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
- Are the eigenvalues of $AB$ equal to the eigenvalues of $BA$?
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 Theorem 1 3 20 in the first edition
- What is the difference between singular value and eigenvalue?
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
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