dbo:abstract |
In mathematics, the method of equating the coefficients is a way of solving a functional equation of two expressions such as polynomials for a number of unknown parameters. It relies on the fact that two expressions are identical precisely when corresponding coefficients are equal for each different type of term. The method is used to bring formulas into a desired form. (en) Der Koeffizientenvergleich ist ein Verfahren aus der linearen Algebra, bei dem die Koeffizienten von zwei Linearkombinationen einer linear unabhängigen Teilmenge eines Vektorraums verglichen werden. Häufig verwendet wird ein Polynomraum als Vektorraum mit Monomen als linear unabhängige Teilmenge, zum Beispiel bei der Partialbruchzerlegung. Man verwendet dabei die Tatsache, dass zwei Linearkombinationen derselben linear unabhängigen Teilmenge genau dann gleich sind, wenn die entsprechenden Koeffizienten gleich sind. (de) Igualar coeficientes é um método de resolução de problemas de álgebra para polinômios iguais, com parâmetros (coeficientes) desconhecidos. O método se baseia no fato de que dois polinômios são iguais quando todos os coeficientes correspondentes são iguais. O procedimento é válido para equações linearmente independentes num espaço vetorial. (pt) |
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https://archive.org/details/encyclopediamath00tant_807 https://archive.org/details/encyclopediamath00tant_807/page/n170 |
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rdfs:comment |
In mathematics, the method of equating the coefficients is a way of solving a functional equation of two expressions such as polynomials for a number of unknown parameters. It relies on the fact that two expressions are identical precisely when corresponding coefficients are equal for each different type of term. The method is used to bring formulas into a desired form. (en) Der Koeffizientenvergleich ist ein Verfahren aus der linearen Algebra, bei dem die Koeffizienten von zwei Linearkombinationen einer linear unabhängigen Teilmenge eines Vektorraums verglichen werden. Häufig verwendet wird ein Polynomraum als Vektorraum mit Monomen als linear unabhängige Teilmenge, zum Beispiel bei der Partialbruchzerlegung. Man verwendet dabei die Tatsache, dass zwei Linearkombinationen derselben linear unabhängigen Teilmenge genau dann gleich sind, wenn die entsprechenden Koeffizienten gleich sind. (de) Igualar coeficientes é um método de resolução de problemas de álgebra para polinômios iguais, com parâmetros (coeficientes) desconhecidos. O método se baseia no fato de que dois polinômios são iguais quando todos os coeficientes correspondentes são iguais. O procedimento é válido para equações linearmente independentes num espaço vetorial. (pt) |
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Koeffizientenvergleich (de) Equating coefficients (en) Igualar coeficientes (pt) |
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