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Algebraic closure. In mathematics, particularly abstract algebra, an algebraic closure of a field K is an algebraic extension of K that is algebraically closed. It is one of many closures in mathematics. Using Zorn's lemma [1] [2] [3] or the weaker ultrafilter lemma, [4] [5] it can be shown that every field has an algebraic closure, and that ...
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Algebraic expression. In mathematics, an algebraic expression is an expression built up from constants (usually, rational or algebraic numbers) variables, and the basic algebraic operations: addition (+), subtraction (-), multiplication (×), division (÷), whole number powers, and roots ( fractional powers). [ 1][ 2] [ 3] [better source needed].
Algebraic equation. In mathematics, an algebraic equation or polynomial equation is an equation of the form , where P is a polynomial with coefficients in some field, often the field of the rational numbers. For example, is an algebraic equation with integer coefficients and. is a multivariate polynomial equation over the rationals.
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The algebraic connectivity (also known as Fiedler value or Fiedler eigenvalue after Miroslav Fiedler) of a graph G is the second-smallest eigenvalue (counting multiple eigenvalues separately) of the Laplacian matrix of G. [1] This eigenvalue is greater than 0 if and only if G is a connected graph. This is a corollary to the fact that the number ...
July 18, 2024 at 3:12 PM. "Hearst Magazines and Yahoo may earn commission or revenue on some items through these links." Denise Austin shares her go-to “low-impact” exercises for women over 50 ...