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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 ...
Mr. Reagan (a.k.a. Cypher) (played by Joe Pantoliano) is a central character in The Matrix.In the film, he regrets being "unplugged" and entering the real world. He betrays the crew of the Nebuchadnezzar, offering to give up Morpheus to the Agents in exchange for being inserted back into the Matrix with no memory of his time outside the Matrix.
List of Where the Red Fern Grows characters; List of characters played by multiple actors in the same film; List of fictional cats in film; List of fictional primates in film; List of films with LGBT characters; List of The Godfather series characters; List of minor characters in The Matrix series; List of original characters in The Hobbit film ...
Synonym for binary matrix or logical matrix. Alternant matrix: A matrix in which successive columns have a particular function applied to their entries. Alternating sign matrix: A square matrix with entries 0, 1 and −1 such that the sum of each row and column is 1 and the nonzero entries in each row and column alternate in sign. Anti-diagonal ...
Alexandre-Théophile Vandermonde (28 February 1735 – 1 January 1796) was a French mathematician, musician, and chemist who worked with Bézout and Lavoisier; his name is now principally associated with determinant theory in mathematics. He was born in Paris, and died there.
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 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.
The identity is named after Alexandre-Théophile Vandermonde (1772), although it was already known in 1303 by the Chinese mathematician Zhu Shijie. [1] There is a q-analog to this theorem called the q-Vandermonde identity. Vandermonde's identity can be generalized in numerous ways, including to the identity