What is the importance of eigenvalues/eigenvectors?
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 …
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 these …
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 dimensions of …
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 all the other …
Can the zero vector be an eigenvector for a matrix?
Oct 25, 2014 · I was checking over my work on WolfRamAlpha, and it says one of my eigenvalues (this one with multiplicity 2), has an eigenvector of (0,0,0). How can the zero vector be an eigenvector?
linear algebra - What are the relations between eigenvectors of $A
Jun 13, 2021 · There is a very important orthogonality relation between eigenvectors of a matrix and its adjoint which is very useful in many applications (reduction of differential equations for example).
Eigenvalues and "Eigenvectors" of Linear Transformations
Jan 5, 2011 · Eigenvalues and "Eigenvectors" of Linear Transformations Ask Question Asked 14 years, 11 months ago Modified 8 years, 2 months ago
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 …
Same eigenvalues, different eigenvectors - Mathematics Stack Exchange
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 returns different …
Fast way to calculate Eigen of 2x2 matrix using a formula
The quadratic formula is actually correct on the Harvard site. It's just a different way of writing it.