Suppose that x is a complex number and i is a non negative integer. Define N - i(x)=|x| i if i is even and N - i(x)=x|x| i-1 if i is odd. Let V - n(x 1, ...,x n) denote the ...Suppose that x is a complex number and i is a non negative integer. Define N - i(x)=|x| i if i is even and N - i(x)=x|x| i-1 if i is odd. Let V - n(x 1, ...,x n) denote the n× n matrix whose (i,j) th entry is N - i-1 (x j) . This paper presents a computation formula for det V - n(x 1, ...,x n) , which can be considered as a generalized that of Vandermonde determinant, and some its important theoretical applications.展开更多
文摘Suppose that x is a complex number and i is a non negative integer. Define N - i(x)=|x| i if i is even and N - i(x)=x|x| i-1 if i is odd. Let V - n(x 1, ...,x n) denote the n× n matrix whose (i,j) th entry is N - i-1 (x j) . This paper presents a computation formula for det V - n(x 1, ...,x n) , which can be considered as a generalized that of Vandermonde determinant, and some its important theoretical applications.
