Showing papers in "Linear Algebra and its Applications in 2020"

TL;DR: In this paper, a generalized tensor function according to the tensor singular value decomposition (T-SVD) is defined, from which the projection operators and Moore-Penrose inverse of tensors are obtained.

TL;DR: In this article, a more natural Hermitian adjacency matrix for directed and partially-directed graphs is introduced, and the purpose of this note is to bring this new Hermitians to the attention of researchers in algebraic graph theory.

TL;DR: In this paper, the authors give necessary and sufficient conditions for two orthogonal semi-Hilbertian operators to satisfy Pythagoras' equality and derive new upper and lower bounds for the numerical radius of operators.

TL;DR: This paper shows that this family produces F q -linear MRD-codes of F q 6 × 6, with the same properties, also in the remaining q odd cases, but not in the q even case, and proves that the corresponding maximum scattered FQ -linear sets of PG are not P Γ L ( 2, q 6 ) -equivalent to any previously known linear set.

TL;DR: This paper studies the problem of finding a nonnegative factorization B B T of a given completely positive matrix A, formulate this factorization problem as a nonconvex feasibility problem and develop a solution method based on alternating projections.

TL;DR: In this article, the Laplacian eigenvalues of the zero divisor graph Γ ( Z n ) of the ring Z n were studied and it was shown that Γ( Z n t ) is integral for every prime p and positive integer t ≥ 2.

TL;DR: In this article, the authors provided bounds and characterizations on the number of roots of linearized polynomials of the form a x + b 0 x q s + b 1 x q S + n + b 2 x Q S + 2 n + 1 + b t − 1 x Q s + n (t − 1 ) ∈ F q n t [x ], with gcd ⁡ ( s, n ) = 1.

TL;DR: This paper presents a spectral algorithm which recovers the clusters exactly with high probability, given mild conditions on n, k, p, q, and d.

TL;DR: In this paper, the atomic structure and arithmetic properties of a monoid M in C are connected to the combinatorics and geometry of its conic hull cone (M ) ⊆ F ⊗ Z gp (M ), where gp(M ) is the Grothendieck group of M.

TL;DR: In this article, it was shown that the Kronecker fast Johnson-Lindenstrauss transform (KFJLT) is a Johnson-LSTM transform, which had previously only been conjectured.

TL;DR: In this paper, a tight upper bound for ρ (G ) in terms of the vertex degrees of G for α ≠ 1 was presented, which holds if and only if G is regular or bipartite semi-regular.

TL;DR: In this paper, the authors characterized the maximal signless Laplacian spectral radius of a graph among all graphs with given size and clique number, and showed that the graph with maximal SLR has the largest eigenvalue of its SLR.

TL;DR: The total energy summing all matrix elements g(x,y) is equal to the Euler characteristic X(G) of G and that the number of positive minus thenumber of negative eigenvalues of L isequal to X( G).

TL;DR: It is shown that the native difficult optimization problems for CPD/TD of Q-order Tensors can be efficiently solved using the TT decomposition according to flexible strategies that involve Q − 2 optimization problems with 3-order tensors.

TL;DR: In this paper, the authors define the phases of a complex sectorial matrix to be its canonical angles, which are uniquely determined from a sectorial decomposition of the matrix, and investigate the rank of I + A B with phase information of A and B, which plays a crucial role in feedback stability analysis.

TL;DR: In this paper, the ABC spectral radius of general graphs has been shown to be a function of the eigenvalues of the ABC eigenvectors of the graph, and some bounds for the spectral radius have been established.

TL;DR: In this paper, a lower bound for the rank of the Hadamard product of positive semidefinite matrices has been shown to be singular in the presence of the Kruskal rank.

TL;DR: Lower bounds for the smallest singular value of rectangular, multivariate Vandermonde matrices with nodes on the complex unit circle were shown in this paper, where the nodes are off the grid, groups of nodes cluster, and the studied minimal singular value is bounded below by the product of inverted distances of a node to all other nodes in the specific cluster.

TL;DR: In this article, the authors studied the properties of operator tuples on a complex Hilbert space H when a semi-inner product induced by a positive operator A on H is considered.

TL;DR: In this article, an upper bound on λ n (A α ) in terms of n, m and α ( 1 / 2 ≤ α ≤ 1 ) was presented, where α ≠ 1 / χ.

TL;DR: A graph unsymmetric Laplacian matrix that operates a diffusive process biased towards low-degree nodes is defined and it is proved that this matrix is positive semidefine with all eigenvalues real and that the rate of convergence of a diffusion depends on the first nontrivial eigenvalue of this LaPLacian.

TL;DR: In this article, it was shown that for a unicyclic graph G of order n ≥ 4, 2 = ν 1 (C n ) ≤ ν 2 (G ) ≤ (S n + e ), with equality if and only if G ≅ C n for the lower bound, and if only if S n+e for the upper bound.

TL;DR: In this article, a complete and rigorous theory of root polynomials of arbitrary matrix polynomial was developed, and the extremality properties of such maximal sets were analyzed.

TL;DR: It is shown that the sequence of dimensions of the linear spaces generated by a given rank-metric code together with itself under several applications of a field automorphism are invariants for the whole equivalence class of the code, which give rise to easily computable criteria to check if two codes are inequivalent.

TL;DR: In this article, a new conjecture on spectral extremal value involving fans and wheels was proposed and proved to be true for k = 2 for the case of n = 2 and n = 3.

TL;DR: A new method to determine the minimality and identifiability of a Waring decomposition A of a specific form T in three variables based on the Hilbert function of A, which can distinguish between forms in the span of the Veronese image of A.

TL;DR: The representation problem of finite-dimensional Markov matrices in Markov semigroups is revisited, with emphasis on concrete criteria for matrix subclasses of theoretical or practical relevance, such as equal-input, circulant, symmetric or doubly stochastic matrices.

TL;DR: In this paper, it was shown that all nonzero eigenvalues of a generalized power hypergraph H s k can be computed from the eigen values of its base hypergraph and of its subgraphs.

TL;DR: In this paper, it was shown that if A is a bounded linear operator on a complex Hilbert space, then 1 2 ω 2 (A + A ⁎ ) + 1 8 ω(A + ε ) (A − ε) ≤ ω ( ⋅ ) and ε(⋅) are the numerical radius and the usual operator norm, respectively.