| The Exact Value of det Vn-(x1,...,xn) and Its Applications |
| Received:October 29, 1995 |
| Key Words:
generalized Vandermonde determinant computation formula generalized Vandermonde matrix rank Tcbebycheff system.
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| Fund Project:Supported by the Science Foundation of Shanxi for Returned Scholars. |
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| Abstract: |
| Suppose that x is a complex number and i is a non negative integer. Define Ni-(x)=|x|i if i is even and Ni-(x)=x|x|i-1 if i is odd. Let Vn-(x1,...,xn) denote the n× n matrix whose (i,j) th entry is Ni-1-(xj) . This paper presents a computation formula for det Vn-(x1,...,xn) , which can be considered as a generalized that of Vandermonde determinant, and some its important theoretical applications. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.1998.04.006 |
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