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Displaying 81 – 100 of 133

Positivity in Complex Spaces and Its Application to Gershgorin Discs.

C. Zenger (1984)

Numerische Mathematik

Positivity of operator-matrices of Hua-type.

Ando, Tsuyoshi (2008)

Banach Journal of Mathematical Analysis [electronic only]

Positivity with Respect to the Round Cone

Miroslav Fiedler (1974)

Matematický časopis

Possible isolation number of a matrix over nonnegative integers

LeRoy B. Beasley, Young Bae Jun, Seok-Zun Song (2018)

Czechoslovak Mathematical Journal

Let $ℤ_{+}$ be the semiring of all nonnegative integers and $A$ an $m \times n$ matrix over $ℤ_{+}$ . The rank of $A$ is the smallest $k$ such that $A$ can be factored as an $m \times k$ matrix times a $k \times n$ matrix. The isolation number of $A$ is the maximum number of nonzero entries in $A$ such that no two are in any row or any column, and no two are in a $2 \times 2$ submatrix of all nonzero entries. We have that the isolation number of $A$ is a lower bound of the rank of $A$ . For $A$ with isolation number $k$ , we investigate the possible values of the rank of $A$ ...

Power bounded and exponentially bounded matrices

Jaromír J. Koliha, Ivan Straškraba (1999)

Applications of Mathematics

The paper gives a new characterization of eigenprojections, which is then used to obtain a spectral decomposition for the power bounded and exponentially bounded matrices. The applications include series and integral representations of the Drazin inverse, and investigation of the asymptotic behaviour of the solutions of singular and singularly perturbed differential equations. An example is given of localized travelling waves for a system of conservation laws.

Power indices of trace zero symmetric Boolean matrices

Bo Zhou (2004)

Discussiones Mathematicae - General Algebra and Applications

The power index of a square Boolean matrix A is the least integer d such that Ad is a linear combination of previous nonnegative powers of A. We determine the maximum power indices for the class of n×n primitive symmetric Boolean matrices of trace zero, the class of n×n irreducible nonprimitive symmetric Boolean matrices, and the class of n×n reducible symmetric Boolean matrices of trace zero, and characterize the extreme matrices respectively.