Construction of acyclic matrices from spectral data

DOI10.1016/0024-3795(89)90295-4zbMath0661.15024OpenAlexW1996254716MaRDI QIDQ1112923

António Leal-Duarte

Publication date: 1989

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0024-3795(89)90295-4

zbMATH Keywords

treeeigenvaluesHermitian matrixCauchy interlacing inequalitiesacyclic matrices

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Hermitian, skew-Hermitian, and related matrices (15B57)

Related Items (29)

On multiplicities of eigenvalues of a spectral problem on a prolate tree ⋮ Inverse eigenvalue problems for two special acyclic matrices ⋮ The λ − τ structured inverse eigenvalue problem ⋮ Inverse eigenvalue problems for acyclic matrices whose graph is a dense centipede ⋮ Construction of matrices with a given graph and prescribed interlaced spectral data ⋮ On multiplicities of eigenvalues of a boundary value problem on a snowflake graph ⋮ A structured inverse spectrum problem for infinite graphs ⋮ Bordering of symmetric matrices and an application to the minimum number of distinct eigenvalues for the join of graphs ⋮ Realizations of interlacing by tree-patterned matrics ⋮ Diminimal families of arbitrary diameter ⋮ Branch duplication for the construction of multiple eigenvalues in an Hermitian matrix whose graph is a tree ⋮ Dirichlet-Neumann inverse spectral problem for a star graph of Stieltjes strings ⋮ Inverse eigenvalue problems and lists of multiplicities of eigenvalues for matrices whose graph is a tree: The case of generalized stars and double generalized stars. ⋮ Generalized inverse eigenvalue problem for matrices whose graph is a path ⋮ On the eigenvalues of generalized and double generalized stars ⋮ On the relationship between the multiplicities of eigenvalues in finite- and infinite-dimensional problems on graphs ⋮ The inverse characteristic polynomial problem for trees ⋮ Inverse eigenvalue problems associated with spring-mass systems ⋮ Construction of real skew-symmetric matrices from interlaced spectral data, and graph ⋮ The minimax inverse eigenvalue problem for matrices whose graph is a generalized star of depth 2 ⋮ Diameter minimal trees ⋮ Smith normal form and acyclic matrices ⋮ Inverse eigenvalue problem for constructing a kind of acyclic matrices with two eigenpairs. ⋮ Unnamed Item ⋮ The inverse eigenvalue problem for Hermitian matrices whose graphs are cycles ⋮ The maximum multiplicity of the largest \(k\)-th eigenvalue in a matrix whose graph is acyclic or unicyclic ⋮ Reconstructing real symmetric matrices from eigenvalues of finite dimensional perturbations ⋮ Minimum-rank matrices with prescribed graph ⋮ The Number of Interlacing Equalities Resulting from Removal of a Vertex from a Tree

Cites Work

• Unnamed Item
• Unnamed Item
• The numerically stable reconstruction of Jacobi matrices from spectral data
• The reconstruction of bordered-diagonal and Jacobi matrices from spectral data
• Inverse eigenvalue problems for Jacobi matrices
• The behavior of eigenvalues and singular values under perturbations of restricted rank
• Construction of a Jacobi matrix from spectral data
• The numerically stable reconstruction of a Jacobi matrix from spectral data
• On the eigenvalues of non-negative Jacobi matrices
• Finite sequences of orthogonal polynomials connected by a Jacobi matrix
• On the construction of a Jacobi matrix from spectral data
• Principal submatrices of normal and Hermitian matrices
• Matrices with prescribed characteristic polynomials and a prescribed submatrix. I, II
• Imbedding Conditions for Hermitian and Normal Matrices
• On Orthogonal Polynomials
• Matrices with Prescribed Characteristic Roots and Diagonal Elements
• A survey of matrix inverse eigenvalue problems
• The Construction of Jacobi and Periodic Jacobi Matrices With Prescribed Spectra
• On the Eigenvalues and Eigenvectors of a Class of Matrices

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