Multinomial matrices
Document Type
Article
Publication Date
8-1986
Department
Department of Mathematical Sciences
Abstract
The paper contains two theorems about multinomial matrices. In the first one it is shown that Mn,q,γ = (mα,β) with mα,β = αβ11·α βqq, α, β, γ ε{lunate} Zq+, 0≤γi ≤αi, γi≤βi, and Σqi=1 αi = Σqi=1 βi = n is nonsingular. In the second one we give explicit expressions for the eigenvalues of D = (dα,β) with dα,β = (nβ)αβ1 1·αβqq, α, β ε{lunate} Zq+, and Σqi = 1 αi = Σqi=1 βi = n. The Bernstein operators from approximation theory are generalized and used to obtain the results of the second theorem.
Publication Title
Discrete Mathematics
Recommended Citation
Shelton, R.,
Heuvers, K.,
Moak, D.,
&
Bhaskara Rao, K.
(1986).
Multinomial matrices.
Discrete Mathematics,
61(1), 107-114.
http://doi.org/10.1016/0012-365X(86)90033-6
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/5239