On determinants of Toeplitz-Hessenberg matrices arising in power series
نویسندگان
چکیده
منابع مشابه
Determinants and permanents of Hessenberg matrices and generalized Lucas polynomials
In this paper, we give some determinantal and permanental representations of generalized Lucas polynomials, which are a general form of generalized bivariate Lucas p-polynomials, ordinary Lucas and Perrin sequences etc., by using various Hessenberg matrices. In addition, we show that determinant and permanent of these Hessenberg matrices can be obtained by using combinations. Then we show, the ...
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We consider the Toeplitz matrices and obtain their unique LU factor-izations. As by-products, we get an explicit formula for the determinant of a Toeplitz matrix and the application of inversion of Toeplitz matrices .
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in this paper, we give some determinantal and permanental representations of generalized lucas polynomials, which are a general form of generalized bivariate lucas p-polynomials, ordinary lucas and perrin sequences etc., by using various hessenberg matrices. in addition, we show that determinant and permanent of these hessenberg matrices can be obtained by using combinations. then we show, the ...
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We provide combinatorial interpretations for determinants which are Fibonacci numbers of several recently introduced Hessenberg matrices. Our arguments make use of the basic definition of the determinant as a signed sum over the symmetric group.
متن کاملCounting Determinants of Fibonacci-hessenberg Matrices Using Lu Factorizations
is a Hessenberg matrix and its determinant is F2n+2. Furthermore, a Hessenberg matrix is said to be a Fibonacci-Hessenberg matrix [2] if its determinant is in the form tFn−1 + Fn−2 or Fn−1 + tFn−2 for some real or complex number t. In [1] several types of Hessenberg matrices whose determinants are Fibonacci numbers were calculated by using the basic definition of the determinant as a signed sum...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1978
ISSN: 0022-247X
DOI: 10.1016/0022-247x(78)90080-x