In this paper, we develop a framework of generalized phase retrieval in which one aims to reconstruct a vector x in R or C through quadratic samples x∗A1x, . . . ,x ∗ANx. The generalized phase retrieval includes as special cases the standard phase retrieval as well as the phase retrieval by orthogonal projections. We first explore the connections among generalized phase retrieval, low-rank matr...

The implicit difference approach is used to discretize a class of generalized fractional diffusion equations into series linear equations. By rearranging the as matrix form, separable forcing term and coefficient matrices are shown be low-ranked nonsingular M-matrix structure, respectively. A doubling Smith method with determined optimally iterative parameters presented for solving correspondin...

We show that a matrix is a Hermitian positive semidefinite matrix whose nonzero entries have modulus 1 if and only if it similar to a direct sum of all 1s matrices and a 0 matrix via a unitary monomial similarity. In particular, the only such nonsingular matrix is the identity matrix and the only such irreducible matrix is similar to an all 1’s matrix by means of a unitary diagonal similarity. ...

We investigate nonsingular hypercubes, and prove several results, stating a condition for a hypercube to be the product of hypercubes of smaller dimensions. There is a shortage of higher dimensional nonsingular hypercubes in the literature. However, we show that the product of two nonsingular hypercubes is always nonsingular. Then we show how to construct four-dimensional nonsingular hypercubes...

This paper deals with the following question:whether a ring of matrices or classes over an adequate elementary divisor inherits property adequacy?
 The to being in matrix rings and commutative is studied.Let us denote by $\mathfrak{A}$ $\mathfrak{E}$ domains, respectively. Also $\mathfrak{A}_2$ $\mathfrak{E}_2$ $2 \times 2$ them. We prove that full nonsingular from are singular set $\mathf...

In this paper, we derive new relative perturbation bounds for eigenvectors and eigenvalues regular quadratic eigenvalue problems of the form $\lambda^2 M x + \lambda C K = 0$, where $M$ $K$ are nonsingular Hermitian matrices $C$ is a general matrix. We base our findings on results an equivalent matrix pair $A-\lambda B$. The can be applied to many interesting appearing in applications, such as ...

We examine the security of several digital signature schemes based on algebraic block codes. It is shown that Xinmei’s digital signature scheme cau be totally broken by a known plaintext attack with complexity O(k3), where t is the dimension of the code used in the scheme. Harn and Wang have proposed a modified version of Xinmei’s scheme that prevents selective forgeries. Their scheme is also s...

In classical result, it is known that any P-bundle over a nonsingular curve T can be birationally transformed to P-bundle over a nonsingular curve T by an elementary transformation. Here, we can ask if it is also possible in 3-fold case. In other words, is it true that any nonsingular del Pezzo fibration over a nonsingular curve can be transformed to another nonsingular del Pezzo fibration? In ...

After reminding the de nition of mosaic ranks we estimate them from above for the inverses to band matrices The estimate grows logarithmically with the matrix size The result presented in this note should be compared with the well known descriptions of the inverses to band matrices as semisep arable matrices Our approach still excells in that it holds under much weaker assumptions Introduction ...