Revision as of 11:26, 12 November 2018 edit Sam Sailor (talk \| contribs) Autopatrolled, Extended confirmed users, Page movers, File movers, New page reviewers, Pending changes reviewers, Rollbackers, Temporary account IP viewers 139,120 edits Removing {{orphan}} per WP:O, article has at least three incoming links from other pages in main space - you can help! ← Previous edit		Revision as of 17:44, 2 September 2022 edit undo Logicdavid (talk \| contribs) 89 edits mNo edit summary Next edit →
Line 5: * Step 1: find the [[symmetric matrix]] A which represents q and find its [[characteristic polynomial]] <math>\Delta (t).</math> * Step 2: find the [[eigenvalues]] of A which are the [[Root system\|roots]] of <math>\Delta (t)</math>. * Step 3: for each ~~eigenvalues~~eigenvalue <math>\lambda</math> of A infrom step 2, find an orthogonal basis of its [[eigenspace]]. * Step 4: normalize all eigenvectors in step 3 which then form an orthonormal basis of '''R'''<sup>''n''</sup>. * Step 5: let P be the matrix whose columns are the normalized [[eigenvector]]s in step 4. ~~The~~Then X=PY is the required orthogonal change of coordinates, and the diagonal entries of <math>P^T AP</math> will be the eigenvalues <math>\lambda_{1} ,\dots ,\lambda_{n}</math> which correspond to the columns of P. == References ==

Orthogonal diagonalization: Difference between revisions