Displaying similar documents to “On block triangular matrices with signed Drazin inverse”

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.

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...

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.

On an extension of Fekete’s lemma

Inheung Chon (1999)

Czechoslovak Mathematical Journal

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We show that if a real n × n non-singular matrix ( n ≥ m ) has all its minors of order m - 1 non-negative and has all its minors of order m which come from consecutive rows non-negative, then all m th order minors are non-negative, which may be considered an extension of Fekete’s lemma.