We present a new algorithm for solving an eigenvalue problem for a real symmetric matrix which is a rank-one modification of a diagonal matrix. The algorithm computes each eigenvalue and all components of the corresponding eigenvector with high relative accuracy inO(n)operations. The algorithm is...
eigenvalue of a matrixphr. 方阵的固有值 matrix eigenvalue矩阵特征值,矩阵特征值 characteristics root of a matrix矩阵特征根,矩阵特征根 integration of a matrix矩阵的积分,矩阵的积分 singular values of a matrix矩阵奇异值,矩阵奇异值 diagonal of a matrix(矩)阵的对角线 ...
G Ming,SC Eisenstat - 《Siam J.matrix Anal.appl》 被引量: 279发表: 1994年 Note on a rank-one modification of the singular value decomposition In this paper, we investigate the singular value decomposition (SVD) of Σ+xyH, where Σ is an m×n real diagonal matrix, x∈Cm, and y∈Cn...
In this paper, first we discretize this differential equation by using the finite difference method to obtain a matrix eigenvalue problem of the form Y = Λ Y , where and are Jacobi and diagonal matrices dependent to cross section P (x) , respectively. Then we estimate the ...
SUMMARYIt is well known that the dominant eigenvalue of a real essentially nonnegative matrix is a convex function of its diagonal entries. This convexity is of practical importance in population biology, graph theory, demography, analytic hierarchy process, and so on. In this paper, the concept...
% The diag() function is used to create a diagonal matrix with these eigenvalues as its diagonal elements. Eigenvalues = diag([lambda1, lambda2, lambda3]); % Solve eigenvalue problem [V, ~] = eig(Eigenvalues); For more information on the functions used here, please refer to the followi...
i.e., A is similar to a diagonal matrix. Proof This can be proved using the fact that eigenvectors associated with two distinct eigenvalues are linearly independent and thus they yield an orthogonal basis for ℝn. Unfortunately the result of proposition 1.17 is not always true if some ...
is a diagonal matrix, the diagonal element is an eigenvalue, Z is an orthogonal matrix, and each column vector of Z is a corresponding eigenvector. That is, , where . Interface Definition C interface: void dsyevd_(const char *jobz, const char *uplo, const int *n, double *a, const...
is a diagonal matrix, the diagonal element is an eigenvalue, Z is an orthogonal matrix, and each column vector of Z is a corresponding eigenvector. That is, , where . Interface Definition C interface: void dsyevd_(const char *jobz, const char *uplo, const int *n, double *a, const...
EigenvalueProblems特征值问题