A natural generalization of the classical Moore-Penrose inverse is presented. The so-called S-Moore-Penrose inverse of a m × n complex matrix A, denoted by AS, is defined for any linear subspace S of the matrix vector space Cn×m. The S-Moore-Penrose inverse AS is characterized using either the singular value decomposition or (for the nonsingular square case) the orthogonal complements with resp...

The models of collective decision-making considered in this paper are nonlinear interconnected cooperative systems with saturating interactions. These systems encode the possible outcomes of a decision process into different steady states of the dynamics. In particular, they are characterized by two main attractors in the positive and negative orthant, representing two choices of agreement amon...

Here, we will provide a spectral norm bound for the error of the approximation constructed by the BasicMatrixMultiplication algorithm. Recall that, given as input a m × n matrix A and an n× p matrix B, this algorithm randomly samples c columns of A and the corresponding rows of B to construct a m× c matrix C and a c× p matrix R such that CR ≈ AB, in the sense that some matrix norm ||AB −CR|| is...

In this paper an unscented Kalman filter with guaranteed positive semidefinite state covariance is proposed by calculating the nearest symmetric positive definite matrix in Frobenius norm and is applied to power system dynamic state estimation. The proposed method is tested on NPCC 48-machine 140-bus system and the results validate its effectiveness.

The problem of computing the distance in the Frobenius norm of a given real irreducible tridiagonal matrix T to the algebraic variety of real normal irreducible tridiagonal matrices is solved. Simple formulas for computing the distance and a normal tridiagonal matrix at this distance are presented. The special case of tridiagonal Toeplitz matrices also is considered.

This report is devoted to the proof of the local (asymptotic) quadratic convergence of the serial block-Jacobi EVD algorithm for Hermitian matrices with multiple eigenvalues. At each iteration step, two off-diagonal blocks with the largest Frobenius norm are annihilated which is an extension of the ‘classical’ Jacobi approach to the block case.