An inverse eigenvalue problem of Hermite-Hamilton matrices in structural dynamic model updating.
An inverse matrix formula in the right-quantum algebra.
An inverse matrix of an upper triangular matrix can be lower triangular
In this note we explain why the group of n×n upper triangular matrices is defined usually over commutative ring while the full general linear group is defined over any associative ring.
An inversion formula, matrix functions, combinatorial identities and graphs
Application of the partitioning method to specific Toeplitz matrices
We propose an adaptation of the partitioning method for determination of the Moore-Penrose inverse of a matrix augmented by a block-column matrix. A simplified implementation of the partitioning method on specific Toeplitz matrices is obtained. The idea for observing this type of Toeplitz matrices lies in the fact that they appear in the linear motion blur models in which blurring matrices (representing the convolution kernels) are known in advance. The advantage of the introduced method is a significant...
Applications of the Moore-Penrose inverse in digital image restoration.
Asymptotic variance of functionals of discrete-time Markov chains via the Drazin inverse.
Binary Moore-Penrose inverses of set inclusion incidence matrices.
Block diagonalization
We study block diagonalization of matrices induced by resolutions of the unit matrix into the sum of idempotent matrices. We show that the block diagonal matrices have disjoint spectra if and only if each idempotent matrix in the inducing resolution double commutes with the given matrix. Applications include a new characterization of an eigenprojection and of the Drazin inverse of a given matrix.
Block representations of the Drazin inverse of a bipartite matrix.
Block-Iterative Methods for Consistent and Inconsistent Linear Equations.
Boosting the inverse interpolation problem by a sum of decaying exponentials using an algebraic approach.
Boundary value problems and controllability of linear systems with right invertible operators [Book]
Bounds for the inverses of diagonally dominant pentadiagonal matrices.
Bounds on the subdominant eigenvalue involving group inverses with applications to graphs
Let be an symmetric, irreducible, and nonnegative matrix whose eigenvalues are . In this paper we derive several lower and upper bounds, in particular on and , but also, indirectly, on . The bounds are in terms of the diagonal entries of the group generalized inverse, , of the singular and irreducible M-matrix . Our starting point is a spectral resolution for . We consider the case of equality in some of these inequalities and we apply our results to the algebraic connectivity of undirected...
Brève communication. Une nouvelle caractérisation des matrices
Carathéodory solutions to quasi-linear hyperbolic systems of partial differential equations with state dependent delays
Certain additive decompositions in a noncommutative ring
We determine when an element in a noncommutative ring is the sum of an idempotent and a radical element that commute. We prove that a matrix over a projective-free ring is strongly -clean if and only if , or , or is similar to , where , , and the equation has a root in and a root in . We further prove that is strongly -clean if be optimally -clean.
Certain matrices related to Fibonacci sequence having recursive entries.
Characterization and properties of (Pσ, Q) symmetric and co-symmetric matrices
Let P ∈ ℂmxm and Q ∈ ℂn×n be invertible matrices partitioned as P = [P0 P1 · · · Pk−1] and Q = [Q0 Q1 · · · Qk−1], with P ℓ ∈ ℂm×mℓ and Qℓ ∈ ℂn×nℓ , 0 ≤ ℓ ≤ k − 1. Partition P−1 and Q−1 as [...] where P̂ℓ ∈ ℂmℓ ×m, Q̂ℓ ∈ ℂnℓ×n , P̂ℓPm = δℓmImℓ , and Q̂ℓQm = δℓmInℓ , 0 ≤ ℓ, m ≤ k − 1. Let Zk = {0, 1, . . . , k − 1}. We study matrices A = [...] Pσ(ℓ)FℓQℓ and B = [...] QℓGℓPσ(ℓ), where σ : Zk → Zk. Special cases: A = [...] and B = [...] , where Aℓ ∈ ℂd1×d2 and Bℓ ∈ ℂd2×d1, 0 ≤ ℓ ≤ k − 1.