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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2021 / Cilt: 50 - Sayı: 1

On the trace of powers of square matrices

Kailash M. Patil
Sayfa
14–23
Yayın Tarihi
2022-10-18
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

As a consequence, we also demonstrate the formula for trace of negative powers of a matrix.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Using Cayley-Hamilton equation for matrices, we obtain a simple formula for trace of powers of a square matrix.
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Temel Bulgular & Veri:The formula becomes simpler in particular cases.
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Sonuç & Katkı:As a consequence, we also demonstrate the formula for trace of negative powers of a matrix.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:trace of a matrix · powers of a matrix · Cayley-Hamilton theorem

Abstract

Using Cayley-Hamilton equation for matrices, we obtain a simple formula for trace of powers of a square matrix. The formula becomes simpler in particular cases. As a consequence, we also demonstrate the formula for trace of negative powers of a matrix.

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Bu Makaleye Atıf Yap

Patil, K. M. (2022). On the trace of powers of square matrices. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 1, 14–23. https://ajindex.com/articles/530005

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Kaynakça (6)

  1. Z. Akyuz and S. Halici, On some combinatorial identities involving the terms of generalized Fibonacci and Lucas sequences, Hacet. J. Math. Stat. 42 (4), 431–435, 2013
  2. H. Avron, Counting triangles in large graphs using randomized matrix trace estimation, Proceedings of Kdd-Ldmta’10, 2010
  3. D.J. Karia, K.M. Patil and H.P. Singh, On the sum of powers of square matrices, Oper. Matrices 13 (1), 221–229, 2019
  4. J.K. Merikoski, On the trace and the sum of elements of a matrix, Linear Algebra Appl. 60, 177–185, 1984
  5. V.P. Pugačev, Application of the trace of a matrix to the calculation of its eigenvalues, Ž. Vyčisl. Mat. i Mat. Fiz. 5, 114–116, 1965
  6. A.V. Zarelua, On congruences for the traces of powers of some matrices, Tr. Mat. Inst. Steklova, 263 (Geometriya, Topologiya i Matematicheskaya Fizika. I), 85–105, 2008.