A Link between the Canonical Decomposition in Multilinear Algebra and Simultaneous Matrix Diagonalization
From MaRDI portal
Publication:5296008
DOI10.1137/040608830zbMath1126.15007OpenAlexW2024166170MaRDI QIDQ5296008
Publication date: 31 July 2007
Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/040608830
Monte Carlo methods (65C05) Eigenvalues, singular values, and eigenvectors (15A18) Canonical forms, reductions, classification (15A21)
Related Items (68)
Derandomization and absolute reconstruction for sums of powers of linear forms ⋮ A combined invariant-subspace and subspace identification method for continuous-time state-space models using slowly sampled multi-sine-wave data ⋮ Separability of Hermitian tensors and PSD decompositions ⋮ Estimating multivariate latent-structure models ⋮ Tensor decomposition for learning Gaussian mixtures from moments ⋮ Blind PARAFAC signal detection for polarization sensitive array ⋮ 4D near-field source localization using cumulant ⋮ On the spectral problem for trivariate functions ⋮ Analysis of normal-form algorithms for solving systems of polynomial equations ⋮ Solving phase-field models in the tensor train format to generate microstructures of bicontinuous composites ⋮ A stabilized normal form algorithm for generic systems of polynomial equations ⋮ IDENTIFICATION OF REGRESSION MODELS WITH A MISCLASSIFIED AND ENDOGENOUS BINARY REGRESSOR ⋮ Rank-1 Tensor Properties with Applications to a Class of Tensor Optimization Problems ⋮ On Kruskal's uniqueness condition for the Candecomp/Parafac decomposition ⋮ Canonical polyadic decomposition of third-order tensors: relaxed uniqueness conditions and algebraic algorithm ⋮ New Uniqueness Conditions for the Canonical Polyadic Decomposition of Third-Order Tensors ⋮ Computing the unique CANDECOMP/PARAFAC decomposition of unbalanced tensors by homotopy method ⋮ Tensor Regression with Applications in Neuroimaging Data Analysis ⋮ Simultaneous Diagonalization via Congruence of Hermitian Matrices: Some Equivalent Conditions and a Numerical Solution ⋮ Condition numbers for the tensor rank decomposition ⋮ PARAFAC-based channel estimation and data recovery in nonlinear MIMO spread spectrum communication systems ⋮ On tensors of border rank \(l\) in \({\mathbb C}^{m\times n\times l}\) ⋮ Some convergence results on the regularized alternating least-squares method for tensor decomposition ⋮ Typical ranks for \(m\times n\times (m-1)n\) tensors with \(m \leq n\) ⋮ Effective Criteria for Specific Identifiability of Tensors and Forms ⋮ Grassmann secants, identifiability, and linear systems of tensors ⋮ Identifiability of an X-Rank Decomposition of Polynomial Maps ⋮ A tensor decomposition model for longitudinal microbiome studies ⋮ Randomized Joint Diagonalization of Symmetric Matrices ⋮ The low-rank approximation of fourth-order partial-symmetric and conjugate partial-symmetric tensor ⋮ Simplicity and typical rank results for three-way arrays ⋮ TR-STF: a fast and accurate tensor ring decomposition algorithm via defined scaled tri-factorization ⋮ On Uniqueness and Computation of the Decomposition of a Tensor into Multilinear Rank-$(1,L_r,L_r)$ Terms ⋮ Symmetric Hermitian decomposability criterion, decomposition, and its applications ⋮ Unnamed Item ⋮ Uni-mode uniqueness conditions for CANDECOMP/PARAFAC decomposition of \(n\)-way arrays with linearly dependent loadings ⋮ Orthogonal Connectivity Factorization: Interpretable Decomposition of Variability in Correlation Matrices ⋮ Line search and trust region strategies for canonical decomposition of semi-nonnegative semi-symmetric 3rd order tensors ⋮ The special sign indeterminacy of the direct-fitting Parafac2 model: some implications, cautions, and recommendations for simultaneous component analysis ⋮ Refined methods for the identifiability of tensors ⋮ On the Problem of Decoupling Multivariate Polynomials ⋮ Hermitian Tensor Decompositions ⋮ Solving the Problem of Simultaneous Diagonalization of Complex Symmetric Matrices via Congruence ⋮ Low rank Tucker-type tensor approximation to classical potentials ⋮ Finding a low-rank basis in a matrix subspace ⋮ Sufficient conditions for uniqueness in Candecomp/Parafac and Indscal with random component matrices ⋮ Direction finding via biquaternion matrix diagonalization with vector-sensors ⋮ Iterative methods for the canonical decomposition of multi-way arrays: application to blind underdetermined mixture identification ⋮ A concise proof of Kruskal's theorem on tensor decomposition ⋮ Bilinear factorizations subject to monomial equality constraints via tensor decompositions ⋮ Solving Polynomial Systems via Truncated Normal Forms ⋮ Imposing Independence Constraints in the CP Model ⋮ On uniqueness conditions for Candecomp/Parafac and Indscal with full column rank in one mode ⋮ Generic and typical ranks of multi-way arrays ⋮ Differential-geometric Newton method for the best rank-\((R _{1}, R _{2}, R _{3})\) approximation of tensors ⋮ Fiber Sampling Approach to Canonical Polyadic Decomposition and Application to Tensor Completion ⋮ Homotopy techniques for tensor decomposition and perfect identifiability ⋮ Three-way clustering of multi-tissue multi-individual gene expression data using semi-nonnegative tensor decomposition ⋮ Inertia laws and localization of real eigenvalues for generalized indefinite eigenvalue problems ⋮ Incremental CP Tensor Decomposition by Alternating Minimization Method ⋮ Systems of Polynomial Equations, Higher-order Tensor Decompositions, and Multidimensional Harmonic Retrieval: A Unifying Framework. Part I: The Canonical Polyadic Decomposition ⋮ Coupled Canonical Polyadic Decompositions and (Coupled) Decompositions in Multilinear Rank- $(L_{r,n},L_{r,n},1)$ Terms---Part II: Algorithms ⋮ Multi-Trek Separation in Linear Structural Equation Models ⋮ Newton-type methods for simultaneous matrix diagonalization ⋮ Coupled Canonical Polyadic Decompositions and (Coupled) Decompositions in Multilinear Rank-$(L_r,n,L_r,n,1)$ Terms---Part I: Uniqueness ⋮ A Recursive Eigenspace Computation for the Canonical Polyadic Decomposition ⋮ Decoupling Multivariate Polynomials Using First-Order Information and Tensor Decompositions ⋮ A Semidefinite Relaxation Method for Partially Symmetric Tensor Decomposition
Uses Software
This page was built for publication: A Link between the Canonical Decomposition in Multilinear Algebra and Simultaneous Matrix Diagonalization