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Dia 1 - van der Veld
Dia 1 - van der Veld

... System of equations • These situations are called linear dependence: – Given vectors: x1, x2,…, xn-1 – Another vector xn is linearly dependent if there exists constants α1, α2,…, αn-1 such that: xn= α1x1+α2x2+ …+αn-1xn-1 • Otherwise the vector xn is linearly independent. • In case of linear depende ...
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A system of polynomial equations is a set of simultaneous equations f1 = 0, ..., fh = 0 where the fi are polynomials in several variables, say x1, ..., xn, over some field k.Usually, the field k is either the field of rational numbers or a finite field, although most of the theory applies to any field.A solution is a set of the values for the xi which make all of the equations true and which belong to some algebraically closed field extension K of k. When k is the field of rational numbers, K is the field of complex numbers.
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