Vandermonde matrix with entry (i j) equal to the i-th point raised to power j-1
VandermondeMatrix[{x1, x2, …, xn}]
VandermondeMatrix[{x1, x2, …, xn}, k]
VandermondeMatrix[vmat]
v = VandermondeMatrix[{0.5, 1., 2., 4.}]
→ {{1, 0.5, 0.25, 0.125}, {1, 1., 1., 1.}, {1, 2., 4., 8.}, {1, 4., 16., 64.}}v = VandermondeMatrix[{Subscript[x, 1], Subscript[x, 2], Subscript[x, 3], Subscript[x, 4]}]
→ {{1, Subscript[x, 1], Subscript[x, 1]^2, Subscript[x, 1]^3}, {1, Subscript[x, 2], Subscript[x, 2]^2, Subscript[x, 2]^3}, {1, Subscript[x, 3], Subscript[x, 3]^2, Subscript[x, 3]^3}, {1, Subscript[x, 4], Subscript[x, 4]^2, Subscript[x, 4]^3}}ByteCount[v = VandermondeMatrix[N[Range[123]]]]
→ 369040