Abstract
By means of complete symmetric polynomials this paper gives a new proof for the Vandermonde determinant formula. Another alternative proof for this formula is obtained via the collocation matrices. It also gives a generalized relationship between the Vandermonde, the Pascal and the Stirling matrices. A new approach to obtain the explicit inverse of the Vandermonde matrix is investigated. Closed form expressions for some Vandermonde related determinants are obtained.
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