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| 1 | Eigenvector |
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| 2 | Spectral graph theory |
| In mathematics, spectral graph theory is the study of properties of a graph in relationship to the eigenvalues and eigenvectors of its adjacency matrix. An undirected graph has a symmetric adjacency matrix and therefore has real eigenvalues and a complete set of orthonormal eigenvectors ... | |
| 3 | Rayleigh quotient |
| (the corresponding eigenvector). Similarly, R(A,x) ≤ λ max and R(A,v max ) = λ max The Rayleigh quotient is used in eigenvalue algorithms to obtain an eigenvalue approximation from an eigenvector ... | |
| 4 | Eigenfunction |
| In mathematics, an eigenfunction f of a linear operator A on a function space is an eigenvector of the linear operator; it satisfies for some scalar λ, the corresponding eigenvalue. The existence of eigenvectors is typically a great help in analysing A . For example, f k( x) = e kx is an ... | |
| 5 | Inverse iteration |
| the eigenvector corresponding to this eigenvalue. Once we have a suitable eigenvector approximation ... | |
| 6 | Eigenface |
| Eigenfaces are a set of eigenvectors derived from the covariance matrix of the probability distribution of the high-dimensional vector space of possible faces of human beings . These eigenvectors are... eigenvectors of the covariance matrix of the statistical distribution of face image vectors are then ... | |
| 7 | Eigenvalue algorithm |
| for finding the eigenvalues of a matrix. These eigenvalue algorithms may also find eigenvectors... choosing an initial vector b (either an eigenvector approximation or a random vector) and iteratively... will converge to an eigenvector corresponding to the dominant eigenvalue. In practice, the vector ... | |
| 8 | Spectral theorem |
| y > for all x,y elements of V . Recall that an eigenvector of a linear operator A is a vector x such... orthonormal basis of V consisting of eigenvectors of A . Each eigenvalue is real. This result is of such... follows λ equals its own conjugate and is therefore real. To prove the existence of an eigenvector ... | |
| 9 | Column space |
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| 10 | Diagonal matrix |
| by a i for all i . Eigenvectors, eigenvalues, determinant The eigenvalues of diag( a1 , ..., a n) are a 1, ..., a n. The unit vectors e 1, ..., e n form a basis of eigenvectors. The determinant of... algebra. Because of the simple description of the matrix operation and eigenvalues/eigenvectors given ... | |
| 11 | Karhunen-Loève theorem |
| Lebesgue measure on [ a, b]) has an orthonormal basis of eigenvectors. Let { ei }i be the eigenvectors... eigenvalue corresponding to the eigenvector e i. In the statement of the theorem, the integral defining... eigenvectors of the covariance kernel are easily determined. These are and the corresponding ... | |
| 12 | Matrix decomposition |
| | Eigenvector | Eigenvalue | Least squares regressions | Outer product | Cross product | Dot product ... | |
| 13 | Row space |
| combination | Basis | Column space | Row space | Dual space | Orthogonality | Eigenvector ... | |
| 14 | Schur decomposition |
| the eigenvectors of A and the schur decomposition is called the spectral decomposition. Furthermore ... | |
| 15 | Sturm-Liouville theory |
| eigenfunctions (analogues of eigenvectors) of a Hermitian differential operator in some function... precisely the eigenvalue problem; that is, we are trying to find the eigenvalues λ and eigenvectors u of... u must be linear. Now observe that finding eigenvectors and eigenvalues of A is essentially the same ... |