Abstract
Abstract In this short note, we provide a brief proof for a recent determinantal formula involving a particular family of banded matrices.
Highlights
It was proved recently in [1] that the determinant of the banded matrix, for any integer n ⩾ 4
The proof for this equality is based on several auxiliary results established for particular cases of the matrix (1.1)
The explicit formula for the determinant of the non-symmetric matrices can be applied in efficient computations, since several algorithms have been proposed to improve the efficiency of the determinant computation [4,5]
Summary
It was proved recently in [1] that the determinant of the banded matrix (which is a particular case of a Hessenberg matrix), for any integer n ⩾ 4, (a − 1)2 if n ≡ 0 (mod 4), det An b+1 2a − b if n ≡ 1 (mod 4), if n ≡ 2 (mod 4), (1.2) The proof for this equality is based on several auxiliary results established for particular cases of the matrix (1.1).
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