Displaying similar documents to “A matrix formalism for conjugacies of higher-dimensional shifts of finite type”

On the matrix negative Pell equation

Aleksander Grytczuk, Izabela Kurzydło (2009)

Discussiones Mathematicae - General Algebra and Applications

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Let N be a set of natural numbers and Z be a set of integers. Let M₂(Z) denotes the set of all 2x2 matrices with integer entries. We give necessary and suficient conditions for solvability of the matrix negative Pell equation (P) X² - dY² = -I with d ∈ N for nonsingular X,Y belonging to M₂(Z) and his generalization (Pn) ∑ i = 1 n X ₂ i - d ∑ i = 1 n Y ² i = - I with d ∈ N for nonsingular X i , Y i ∈ M ₂ ( Z ) , i=1,...,n.

Nonsingularity, positive definiteness, and positive invertibility under fixed-point data rounding

Jiří Rohn (2007)

Applications of Mathematics

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For a real square matrix A and an integer d ≥ 0 , let A ( d ) denote the matrix formed from A by rounding off all its coefficients to d decimal places. The main problem handled in this paper is the following: assuming that A ( d ) has some property, under what additional condition(s) can we be sure that the original matrix A possesses the same property? Three properties are investigated: nonsingularity, positive definiteness, and positive invertibility. In all three cases it is shown that there exists...

Nested matrices and inverse M -matrices

Jeffrey L. Stuart (2015)

Czechoslovak Mathematical Journal

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Given a sequence of real or complex numbers, we construct a sequence of nested, symmetric matrices. We determine the L U - and Q R -factorizations, the determinant and the principal minors for such a matrix. When the sequence is real, positive and strictly increasing, the matrices are strictly positive, inverse M -matrices with symmetric, irreducible, tridiagonal inverses.

Complexity of computing interval matrix powers for special classes of matrices

David Hartman, Milan Hladík (2020)

Applications of Mathematics

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Computing powers of interval matrices is a computationally hard problem. Indeed, it is NP-hard even when the exponent is 3 and the matrices only have interval components in one row and one column. Motivated by this result, we consider special types of interval matrices where the interval components occupy specific positions. We show that computing the third power of matrices with only one column occupied by interval components can be solved in cubic time; so the asymptotic time complexity...

On block triangular matrices with signed Drazin inverse

Changjiang Bu, Wenzhe Wang, Jiang Zhou, Lizhu Sun (2014)

Czechoslovak Mathematical Journal

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The sign pattern of a real matrix A , denoted by sgn A , is the ( + , - , 0 ) -matrix obtained from A by replacing each entry by its sign. Let 𝒬 ( A ) denote the set of all real matrices B such that sgn B = sgn A . For a square real matrix A , the Drazin inverse of A is the unique real matrix X such that A k + 1 X = A k , X A X = X and A X = X A , where k is the Drazin index of A . We say that A has signed Drazin inverse if sgn A ˜ d = sgn A d for any A ˜ ∈ 𝒬 ( A ) , where A d denotes the Drazin inverse of A . In this paper, we give necessary conditions for some block triangular matrices...

The Re-nonnegative definite solutions to the matrix equation A X B = C

Qing Wen Wang, Chang Lan Yang (1998)

Commentationes Mathematicae Universitatis Carolinae

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An n × n complex matrix A is called Re-nonnegative definite (Re-nnd) if the real part of x * A x is nonnegative for every complex n -vector x . In this paper criteria for a partitioned matrix to be Re-nnd are given. A necessary and sufficient condition for the existence of and an expression for the Re-nnd solutions of the matrix equation A X B = C are presented.