The eigenvectors tell you about how the ellipse is oriented and the eigenvalues tell you where the ellipse is distorted (where it's flat). If you choose to ignore the "thickness" of the ellipse then …

Feb 23, 2011 · Eigenvalues and eigenvectors are central to the definition of measurement in quantum mechanics Measurements are what you do during experiments, so this is obviously …

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 …

I'm studying eigenvector and eigenvalue but there are some confusing things to me. (1) Eigenvectors are not unique (2) If eigenvectors come from distinct eigenvalues, then …

Any vector subject to the identity matrix will give you the same vector back. That is the property of the identity matrix. But in light of eigenvectors and eigenvalues, this also matches the situation …

Sep 10, 2015 · If I understand correctly you are decoupling the system and inevitably divide through by the eigenvalues for each separate equation because of the diagonal matrix.

Explore related questions linear-algebra eigenvalues-eigenvectors See similar questions with these tags.

using the quadratic formula, $\lambda = 9$ or $\lambda = 4$, so the two eigenvalues are $\ {9,4\}$. when i try to get the eigenvectors, i run into problems. i plugin $\lambda = 9$ into the …

May 8, 2012 · Eigenvectors corresponding to different eigenvalues will be orthogonal if the matrix is symmetric. This is part of the real spectral theorem.

Jul 5, 2015 · This is what I have understood. Please correct me if i am wrong. 1) If a matrix has 1 eigenvalue as zero, the dimension of its kernel may be 1 or more (depends upon the number …