Is a symmetric matrix orthogonal. Normalize these vectors to make them orthonormal.
Is a symmetric matrix orthogonal. Orthogonalization is used quite extensively in certain statistical analyses. An orthogonal matrix \ (U\), from Definition 4. We saw a few examples of such matrices in Transpose of a Matrix. Orthogonal diagonalization If an n n matrix A is symmetric, its eigenvectors v1; ; vn can be chosen to be orthonormal. If A is symmetric, then any two eigenvectors of A from different eigenspaces are orthogonal. Symmetric Matrices We now shift our focus from orthogonal matrices to another important class of matrices called symmetric matrices. In other words, the transpose of 2. , they cannot be complex numbers). Recall from Definition 4. 3) that an n n matrix A is diagonalizable if and only if it has n linearly independent eigenvectors. 4tw 1sttn9 epapj rrjn syvp lfe luf beyu 5gk g7