Trace of Positive Integer Power of Real 2 × 2 Matrices

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.

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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

[1] Brezinski, C., Fika, P. and Mitrouli, M. (2012) Estimations of the Trace of Powers of Positive Self-Adjoint Operators by Extrapolation of the Moments. Electronic Transactions on Numerical Analysis, 39, 144-155.
[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.
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