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On Algebraically Positive Matrices With Associated Sign Patterns

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Abstract

We study algebraically positive matrices and explore some of their interesting properties. We also explore the connections between algebraic positivity and irreducibility and how they relate to the fundamental theorem of Perron-Frobenius theory. Notably, we characterize all 3 × 3 symmetric sign pattern matrices that require algebraic positivity.

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Acknowledgement

Both the authors are thankful to Prof. Jaydeb Sarkar, Indian Statistical Institute, Bangalore, for introducing them to this relatively new yet fascinating subject and for his continuous support and guidance, which helped them through the course of the project. They would also like to express their gratitude to the journal referees for their valuable suggestions and improvements, which greatly helped shape the article’s content.

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Authors and Affiliations

  1. Indian Statistical Institute Statistics and Mathematics Unit (SMU), 8th Mile, Mysore Road, Bangalore, 560 059, India

    Amitakshar Biswas & Soumyajyoti Kundu

Authors
  1. Amitakshar Biswas
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  2. Soumyajyoti Kundu
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Corresponding authors

Correspondence to Amitakshar Biswas or Soumyajyoti Kundu.

Additional information

Amitakshar Biswas is presently a graduate student in statistics at the Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Canada. He completed his B.Math from the Indian Statistical Institute, Bangalore. He is interested in statistics and probability theory.

Soumyajyoti Kundu is presently a graduate student in mathematics at the Department of Mathematics & Statistics, McMaster University, Hamilton, Canada. He completed his B.Math from the Indian Statistical Institute, Bangalore. He is interested in probability theory.

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Biswas, A., Kundu, S. On Algebraically Positive Matrices With Associated Sign Patterns. Reson 27, 1211–1235 (2022). https://doi.org/10.1007/s12045-022-1415-1

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  • DOI: https://doi.org/10.1007/s12045-022-1415-1

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