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ALAMT> Vol.5 No.4, December 2015
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Trace of Positive Integer Power of Real 2 × 2 Matrices

Abstract Full-Text HTML XML Download Download as PDF (Size:302KB) PP. 150-155
DOI: 10.4236/alamt.2015.54015    4,944 Downloads   6,461 Views   Citations
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Jagdish Pahade*, Manoj Jha

Affiliation(s)

Department of Mathematics, Maulana Azad National Institute of Technology, Bhopal, India.

ABSTRACT

The purpose of this paper is to discuss the theorems for the trace of any positive integer power of 2 × 2 real matrix. We obtain a new formula to compute trace of any positive integer power of 2 × 2 real matrix A, in the terms of Trace of A (TrA) and Determinant of A (DetA), which are based on definition of trace of matrix and multiplication of the matrixn times, where n is positive integer and this formula gives some corollary for TrAn when TrA or DetA are zero.

KEYWORDS

Trace, Determinant, Matrix Multiplication

Cite this paper

Pahade, J. and Jha, M. (2015) Trace of Positive Integer Power of Real 2 × 2 Matrices. Advances in Linear Algebra & Matrix Theory, 5, 150-155. doi: 10.4236/alamt.2015.54015.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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[2] Avron, H. (2010) Counting Triangles in Large Graphs Using Randomized Matrix Trace Estimation. Proceedings of Kdd-Ldmta’10, 2010.
[3] Zarelua, A.V. (2008) On Congruences for the Traces of Powers of Some Matrices. Proceedings of the Steklov Institute of Mathematics, 263, 78-98.
[4] Pan, V. (1990) Estimating the Extremal Eigenvalues of a Symmetric Matrix. Computers & Mathematics with Applications, 20, 17-22.
[5] Datta, B.N. and Datta, K. (1976) An algorithm for Computing Powers of a Hessenberg Matrix and Its Applications. Linear Algebra and its Applications, 14, 273-284.
[6] Chu, M.T. (1985) Symbolic Calculation of the Trace of the Power of a Tridiagonal Matrix. Computing, 35, 257-268.
[7] Higham, N. (2008) Functions of Matrices: Theory and Computation. SIAM, Philadelphia.
[8] Michiel, H. (2001) Trace of a Square Matrix. Encyclopedia of Mathematics, Springer.
https://en.wikipedia.org/wiki/Trace_

  
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