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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
- 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
- linear algebra - Invertibility, eigenvalues and singular values . . .
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? Also, what about the "singular values" of a matrix? If there are good online resources which answer these question I would be grateful for any pointers
- Eigenvalues of $A$ and $A A^T$ - Mathematics Stack Exchange
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 $A$,
- 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
- The definition of simple eigenvalue - Mathematics Stack Exchange
There seem to be two accepted definitions for simple eigenvalues The definitions involve algebraic multiplicity and geometric multiplicity When space has a finite dimension, the most used is alge
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