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An m × n rectangular Vandermonde matrix such that m ≤ n has rank m if and only if all x i are distinct. An m × n rectangular Vandermonde matrix such that m ≥ n has rank n if and only if there are n of the x i that are distinct. A square Vandermonde matrix is invertible if and only if the x i are distinct. An explicit formula for the ...
Following is a list of antipsychotics, sorted by class. Antipsychotics. Antipsychotics by class Generic name Brand names Chemical class ATC code
The defining property of the Vandermonde polynomial is that it is alternating in the entries, meaning that permuting the by an odd permutation changes the sign, while permuting them by an even permutation does not change the value of the polynomial – in fact, it is the basic alternating polynomial, as will be made precise below.
A matrix with the only nonzero entries on the main diagonal and the diagonals just above and below the main one. X–Y–Z matrix A generalization to three dimensions of the concept of two-dimensional array: Vandermonde matrix: A row consists of 1, a, a 2, a 3, etc., and each row uses a different variable. Walsh matrix
The matrix X on the left is a Vandermonde matrix, whose determinant is known to be () = < (), which is non-zero since the nodes are all distinct. This ensures that the matrix is invertible and the equation has the unique solution A = X − 1 ⋅ Y {\displaystyle A=X^{-1}\cdot Y} ; that is, p ( x ) {\displaystyle p(x)} exists and is unique.
The roots of the characteristic polynomial () are the eigenvalues of ().If there are n distinct eigenvalues , …,, then () is diagonalizable as () =, where D is the diagonal matrix and V is the Vandermonde matrix corresponding to the λ 's: = [], = [].
Many drugs have more than one name and, therefore, the same drug may be listed more than once. Brand names and generic names are differentiated by capitalizing brand names. See also the list of the top 100 bestselling branded drugs , ranked by sales.
This is an alphabetical list of psychiatric medications used by psychiatrists and other physicians to treat mental illness or distress. The list is not exhaustive. All mentioned drugs here are generic names. Not all drugs listed are used regularly in all countries.