How to intuitively understand eigenvalue and eigenvector?
There is no rotation. These favored vectors are precisely the eigenvectors and the amount by which each of these favored vectors stretches or compresses is the eigenvalue. So why are …
What is the importance of eigenvalues/eigenvectors?
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 …
What is the significance of left and right eigenvectors?
Sep 4, 2023 · The right eigenvectors are eigenvectors for this transformation, but the left ones for $A^T$, which, geometrically can be totally different. However, the eigenvalues and the …
reference request - A simple explanation of eigenvectors and ...
May 3, 2011 · Eigenvectors and Eigenvalues are structures that your brain uses in order to correctly access the incoming trajectory of the ball, given only 2D frames over time. Your mind …
Are all eigenvectors, of any matrix, always orthogonal?
May 8, 2012 · 81 In general, for any matrix, the eigenvectors are NOT always orthogonal. But for a special type of matrix, symmetric matrix, the eigenvalues are always real and eigenvectors …
Eigenvalues and "Eigenvectors" of Linear Transformations
Jan 5, 2011 · Eigenvalues and "Eigenvectors" of Linear Transformations Ask Question Asked 15 years ago Modified 8 years, 3 months ago
linear algebra - Relation between left and right eigenvectors ...
Mar 24, 2016 · Your nice proof of your observation also shows that non-corresponding left and right eigenvectors are orthogonal. So the left eigenvector indicates the hyperplane containing …
linear algebra - How to prove that eigenvectors from different ...
How can I prove that if I have $n$ eigenvectors from different eigenvalues, they are all linearly independent?
Same eigenvalues, different eigenvectors - Mathematics Stack …
Mar 16, 2012 · I'm interested in the case of a specific matrix having different eigenvectors corresponding to two identical eigenvalues. The method I use for spectral decomposition …
When are the Eigenvectors of a A and $A^T$ the same?
Sep 9, 2020 · This seems strange, but eigenvalues are indeed equal, maybe authors just mixed it somehow? For eigenvectors, right eigenvectors of $A^t$ are left eigenvectors of $A$.