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2. Eigendecomposition of a matrix - Wikipedia

   en.wikipedia.org/wiki/Eigendecomposition_of_a_matrix

   Let A be a square n × n matrix with n linearly independent eigenvectors q i (where i = 1, ..., n).Then A can be factored as = where Q is the square n × n matrix whose i th column is the eigenvector q i of A, and Λ is the diagonal matrix whose diagonal elements are the corresponding eigenvalues, Λ ii = λ i.

3. Lanczos algorithm - Wikipedia

   en.wikipedia.org/wiki/Lanczos_algorithm

   The Lanczos algorithm is most often brought up in the context of finding the eigenvalues and eigenvectors of a matrix, but whereas an ordinary diagonalization of a matrix would make eigenvectors and eigenvalues apparent from inspection, the same is not true for the tridiagonalization performed by the Lanczos algorithm; nontrivial additional steps are needed to compute even a single eigenvalue ...

4. QR algorithm - Wikipedia

   en.wikipedia.org/wiki/QR_algorithm

   In the case when the matrix is depicted as a near-circle, the matrix can be replaced with one whose depiction is a perfect circle. In that case, the matrix is a multiple of the identity matrix, and its eigendecomposition is immediate. Be aware though that the resulting eigenbasis can be quite far from the original eigenbasis.

5. Matrix decomposition - Wikipedia

   en.wikipedia.org/wiki/Matrix_decomposition

   For a normal matrix A (and only for a normal matrix), the eigenvectors can also be made orthonormal (=) and the eigendecomposition reads as =. In particular all unitary , Hermitian , or skew-Hermitian (in the real-valued case, all orthogonal , symmetric , or skew-symmetric , respectively) matrices are normal and therefore possess this property.

6. How to Keep Your Dog’s Mind Sharp: 16 Trainer ... - AOL

   www.aol.com/keep-dog-mind-sharp-16-162000270.html

   Many dogs love to sniff around and hunt for things. If your dog is a natural forager and hunter, he’ll love it if you start introducing some fun search games into his daily routine. 9. Treasure Hunt

7. Expert Trainer Explains Why Dogs Growl & How to Handle It - AOL

   www.aol.com/expert-trainer-explains-why-dogs...

   As the dog remains relaxed, it is possible to slowly raise criteria and increase the intensity of the trigger, such as by having the person move more naturally and then practicing in slightly ...