Stephens. Complex eigenvalues of a non-negative matrix with a specified graph. Linear Algebra and Appl., 20(2), (1978), 179-187. 4.1, 4.3C.R. Johnson, R.B. Kellog, A.B. Stephens, Complex eigenvalues of a nonnegative matrix with a specified graph. II, Linear Multilinear Algebra 7 (...
Then G(A) is the Lie algebra associated with the complex matrix A. The above maximal ideal τ∈G~(A) satisfies τ=(τ∩η~−)⊕(τ∩η~+). We denote the elements ei,fi,h by the same notation in both G(A) and G~(A). ...
From this we see that a complex matrix with complex eigenvalues and complex eigenvectors corresponds to projecting a real vector onto orthogonal planes and then rotating and dilating the projected vectors. This geometric interpretation is analogous to the corresponding interpretation for an N × N real...
For example, the non-Hermitian systems with complex eigenvalues, it’s interesting to explore whether the power-law scree plots exist in non-Hermitian systems or not, which is also a promising future direction. Finally, as stated in the “Introduction” section, the spirit of SVD is to view...
In summary, the four distinct cases are three distinct eigenvalues; one real, distinct eigenvalue and two real, repeated eigenvalues; one real, repeated eigenvalue with multiplicity 3; and one real, distinct eigenvalue and two complex conjugate eigenvalues. We shall now consider the matrix A=(1...
最后,通过证明得到一类特征值是关于实轴和虚轴对称的复Hamilton矩阵.In this paper, we focus on the conditions under which the eigenvalues of complex Hamiltonian matrices are symmetric with respect to the real and imaginary axis, and the sufficient conditions that the eigenvalues of complex Hamiltonian ...
Hermitian matrices are a useful generalization of symmetric matrices for complex matrices. A matrix that is not symmetric is said to be an asymmetric matrix, not to be confused with an antisymmetric matrix. A matrix can be tested to see if it is symmetric in the Wolfram Language using ...
Tensor calculus. rust interpolation linear-algebra mathematics special-functions scientific-computing quadrature differential-equations eigenvectors sparse-matrix numerical-integration eigenvalues quadrature-integration spectral-methods bessel-function numerical-derivatives gamma-function Updated Apr 14, 2025 Rust ...
Remarkably, if r is a vector of length n, a random sparse matrix with eigenvalues equal to the elements of r is produced. Eigenvalues are discussed in Section 2.15. A positive definite matrix has all its eigenvalues positive and consequently such a matrix can be generated by choosing each of...
An anti-circulant tensor C of order m and dimension n with the compressed generating vector c has a Z-/H-eigenvector 1n1, and the corresponding Z- and H-eigenvalues are nm−221⊤c and nm − 21⊤c, respectively. When n is even, it has another Z-eigenvector 1n1~, where 1~...