We initiate a systematic study of the Row Deletion(B) problem on matrices: For a fixed “forbidden submatrix” B, the question is, given an input matrix A (both A and B have entries chosen from a finite-size alphabet), to remove a minimum number of rows such that A has no submatrix which is equivalent to a row or column permutation of B. An application of this question can be found, e.g., in the ...

Abstract—Image or document encryption is needed through egovernment data base. Really in this paper we introduce two matrices images, one is the public, and the second is the secret (original). The analyses of each matrix is achieved using the transformation of singular values decomposition. So each matrix is transformed or analyzed to three matrices say row orthogonal basis, column orthogonal ...

In this article, we present results on Toeplitz matrices with Oresme numbers components. First, the components are created and then Frobenius(Euclidian), row column norms of these found. Furthermore lower upper bounds obtained for spectral matrices. addition, Frobenius Kronecker Hadamard product calculated.

The row (resp. column) rank profile of a matrix describes the stair-case shape of its row (resp. column) echelon form. We here propose a new matrix invariant, the rank profile matrix, summarizing all information on the row and column rank profiles of all the leading sub-matrices. We show that this normal form exists and is unique over any ring, provided that the notion of McCoy’s rank is used, ...

The irregular nature of the data structures required to efficiently store arbitrary sparse matrices and the architectural constraints of a SIMD computer make it difficult to design an algorithm that can efficiently multiply an arbitrary sparse matrix by a vector. A new ‘‘block-row’’ algorithm is proposed. It allows the ‘‘regularity’’ of a data structure with a row-major mapping to be varied by ...

Motivated by the observation that there exists one-to-one correspondence between column space decompositions and row space decompositions of a matrix, the class of matrices dominated by this matrix under ‘≤’ is characterized in terms of characteristic of column space decompositions, where ≤ is a matrix partial order such as the star partial order, the sharp partial order, and the core partial o...