I'm a little confused as to when a matrix is orthogonally diagonalizable. I understand that if symmetric, it's always orthogonally diagonalizable, but in what other cases can you orthogonally

Jul 8, 2016 · I am studying some linear algebra and I've learned one algorithm to transform a bilinear symmetric form in a diagonal matrix, i.e., it is a sum of squares. But to do this, I am …

Jan 30, 2021 · $\begingroup$ You start with a general 2 by 2 matrix, and then when you go for a guess you start with a particular 2 by 2 matrix. That won't give you the general power. …

Jul 8, 2015 · There are several ways to decide whether matrix has independent set of eigenvectors that can span the entire space. One is that if matrix has distinct eigenvalues, it …

May 10, 2015 · Your initial assumption on which your whole question is constructed is mistaken: one cannot diagonalize the metric tensor locally in general (or else every Riemann manifold …

Alright, here is a "regular" ternary form with integer matrix, $$ 3 x^2 + 3 y^2 + 5 z^2 - 4 yz + 2 zx + 2 xy, $$ symmetric matrix $$ \left( \begin{array}{rrr} 3 & 1 & 1 \\ 1 & 3 & -2 \\ 1 & -2 & 5 …

Mar 28, 2020 · $\begingroup$ @HossienSahebjame no thats not the precise definition. the part where you say the diagonal entries and the columns of B consist of the eigenvectors of B are …

Second thing is that Diagonalizable does'nt mean n distinct eigenvalues.for example identity matrix has repeated eigenvalues still it is diagonalizable. Share Cite

$\begingroup$ This does or does not mean it can't be diagonalized, depending on whether you're supposed to be allowed to use complex eigenvectors or not. We can't say, you need to ask the …

May 15, 2015 · However in writing the matrix in this nice diagonal form you have to express it w.r.t. a new eigenvector basis. But you'll probably want the answer of your matrix multiplication …