# Eigenvectors

### Some articles on eigenvectors, eigenvector:

Phase Plane Method - Example of A Linear System - Solving Using Eigenvalues
... λ, given by the determinant and eigenvectors The eigenvalues represent the powers of the exponential components and the eigenvectors are coefficients ... Due to the nonuniqueness of eigenvectors, every solution arrived at in this way has undetermined constants c1, c2.. ... solution is where λ1 and λ2 are the eigenvalues, and (k1, k2), (k3, k4) are the basic eigenvectors ...
Modal Matrix
... process involving eigenvalues and eigenvectors ... Specifically the modal matrix M is the n×n matrix formed with the eigenvectors of A as columns in M ... the eigenvalues should appear left→right top→bottom in the same order as its eigenvectors are arranged left→right into M) ...
Eigendecomposition Of A Matrix - Eigendecomposition of A Matrix
... A can be factorized as where Q is the square (N×N) matrix whose ith column is the eigenvector of A and Λ is the diagonal matrix whose diagonal elements are the corresponding eigenvalues, i.e ... The eigenvectors are usually normalized, but they need not be ... A non-normalized set of eigenvectors, can also be used as the columns of Q ...
Time-evolving Block Decimation - The Update of The Decomposition - Two-qubit Gates Acting On Qubits k, K+1
... belonging to only four subsystems The subspace J is spanned by the eigenvectors of the reduced density matrix In a similar way, the subspace K is spanned by the eigenvectors of ... at the bond k and their corresponding Schmidt eigenvectors must be computed and expressed in terms of the 's of the decomposition D ... Expressing the eigenvectors of the diagonalized matrix in the basis the 's are obtained as well From the left-hand eigenvectors, after expressing them in the basis, the 's are ...
Compact Operator On Hilbert Space - Compact Self Adjoint Operator - Spectral Theorem
... on a real or complex Hilbert space H, there exists an orthonormal basis of H consisting of eigenvectors of T ... of T admits, either a finite orthonormal basis of eigenvectors of T, or a countably infinite orthonormal basis {en} of eigenvectors of T, with ... orthonormal basis for the kernel of T, and obtain an orthonormal basis {fn} for H, consisting of eigenvectors of T with real eigenvalues {μn} such that μn → 0 ...