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Trace of Positive Integer Power of Real 2 × 2 Matrices

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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*(Tr*A*) and Determinant of*A*(Det*A*), 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 Tr*A*when Tr^{n}*A*or Det*A*are zero.KEYWORDS

Conflicts of Interest

The authors declare no conflicts of interest.

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.

[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. https://en.wikipedia.org/wiki/Trace_ |

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