Expressions for the integer powers of the Min matrix

Subject Areas : Linear and multilinear algebra; matrix theory

M. Beiranvand ¹ , M. Ghasemi Kamalvand ²

1 - Department of Mathematics, Lorestan University, Khorramabad, Iran
2 - Department of Mathematics, Lorestan University, Khorramabad, Iran

Received: 2022-07-10 Accepted : 2022-09-29 Published : 2022-09-01

Keywords: Eigenvalues, eigenvectors, integer powers, Min matrix,

Abstract :

‎In this paper‎, ‎we derive the general expression for the entries of the positive integer powers of the Min matrix $A=[\text{min}\{i,j\}];\; i,j=1,2,\cdots,n$ of arbitrary order‎. ‎Also‎, ‎we give Maple 18 procedures in order to verify our calculations‎.

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