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Publications Influence

Bounds for the Perron root of a nonnegative matrix involving the properties of its graph

- Yu. A. Al’pin
- Mathematics
- 1 October 1995

15 2

A simple proof for the inequality between the perron root of a nonnegative matrix and that of its geometric symmetrization

- Yu. A. Al’pin, J. Merikoski
- Mathematics
- 8 September 2010

AbstractLet A = (aij) be a nonnegative square matrix, let G = (gij) be its geometric symmetrization, i.e., gij = $$
\sqrt {a_{ij} a_{ji} }
$$, and let ρ denote the Perron root. We present a simple… Expand

5 1

A criterion for unitary congruence between matrices

- Yu. A. Al’pin, K. Ikramov
- Mathematics
- 15 May 2011

7 1

Combinatorial properties of irreducible semigroups of nonnegative matrices

- Yu. A. Al’pin, V. S. Al'pina
- Mathematics
- 19 April 2013

The paper suggests a combinatorial proof of the Protasov–Voynov theorem on an irreducible semigroup of nanonegative matrices free of positive matrices. This solves the problem posed by the authors of… Expand

17

Combinatorial Properties of Entire Semigroups of Nonnegative Matrices

- Yu. A. Al’pin, V. S. Al'pina
- Mathematics
- 19 May 2015

Generalizations of the Protasov–Voynov theorem on the structure of irreducible semigroups of nonnegative matrices free of zero rows and columns are obtained. The theorem is extended to semigroups… Expand

7

The generalized monotonicity property of the Perron root

- Yu. A. Al’pin, L. Y. Kolotilina
- Mathematics
- 1 March 2007

The paper presents a new monotonicity property of the Perron root of a nonnegative matrix. It is shown that this new property implies known monotonicity properties and also the Chistyakov two-sided… Expand

4

On the Simultaneous Triangulability of Matrices

- Yu. A. Al’pin, N. A. Koreshkov
- Mathematics
- 1 November 2000

Two necessary and sufficient criteria for the simultaneous triangulability of two complex matrices are established. Both of them admit a finite verification procedure. To prove the first criterion,… Expand

7

A New Proof of the Protasov-Voynov Theorem on Semigroups of Nonnegative Matrices

- Yu. A. Al’pin, V. S. Al’pina
- Mathematics
- 1 May 2019

A new combinatorial proof of the Protasov-Voynov theorem on the structure of irreducible semigroups of nonnegative matrices is proposed. The original proof was obtained by geometric methods.

2

Combinatorial structure of k-semiprimitive matrix families

- Yu. A. Al’pin, V. S. Al’pina
- Mathematics
- 31 May 2016

Protasov's Theorem on the combinatorial structure of k-primitive families of non-negative matrices is generalized to k-semiprimitive matrix families. The main tool is the binary relation of colour… Expand

2

Bounds for joint spectral radii of a set of nonnegative matrices

- Yu. A. Al’pin
- Mathematics
- 26 March 2010

Bounds for joint spectral radii of a set of nonnegative matrices are established by using the apparatus of idempotent algebra.

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