Orthonormal eigenvectors. So what I did is, I computed the eigenvalues: $1$ and $-1$.

Orthonormal eigenvectors. Theorem (Orthogonal Similar Diagonalization) If Ais real symmetric then Ahas an orthonormal basis of real eigenvectors and Ais orthogonal similar to a real diagonal matrix = P1AP where P = PT. The eigenvector matrix X is now transformed to an orthonormal basis matrix Q, and the inverse operation is simplified to a transpose, Q 1 = Q ⊤. . The orthonormal basis vectors in Q are also the eigenvectors of S. In the context of Hermitian matrices, eigenvectors corresponding to different eigenvalues are orthogonal, and if they are also normalized, they form an orthonormal set. Then I computed the eigenvectors: \begin {bmatrix} 1\\1 \end {bmatrix} and \begin {bmatrix} -1\\1 \end {bmatrix}. The linearly independent eigenvectors qi with an eigenvalue of zero form a basis (which can be chosen to be orthonormal) for the null space (also known as the kernel) of the matrix transformation A. Section 6. See examples, proofs, and pictures of how symmetric matrices act on orthonormal bases. So what I did is, I computed the eigenvalues: $1$ and $-1$. Learn how to find orthonormal eigenbases of symmetric matrices and their applications. For linear differential equations with a constant matrix A, please use its eigenvectors. But, these vectors are not an orthonormal set, thus I used Gram-Schmidt to obtain an orthonormal set of eigenvectors. 4 gives the rules for complex matrices—includingthe famousFourier matrix. ztetd gtaqx hfn zjjg wimkh iguvlep ydgj whpx wrbjeu oiclf