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 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 of central …
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 is able to …
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 AT A T, which, geometrically can be totally different. However, the eigenvalues and the dimensions of their …
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
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 …
Why is the eigenvector of a covariance matrix equal to a principal ...
168 If I have a covariance matrix for a data set and I multiply it times one of it's eigenvectors. Let's say the eigenvector with the highest eigenvalue. The result is the eigenvector or a scaled version of the …
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 - How to prove that eigenvectors from different ...
Closed 3 years ago. How can I prove that if I have n n eigenvectors from different eigenvalues, they are all linearly independent?