Coefficient comparison
The coefficient comparison is a method from linear algebra in which the coefficients of two linear combinations of a linearly independent subset of a vector space are compared. A polynomial space is often used as a vector space with monomials as a linearly independent subset, for example in partial fraction decomposition . One uses the fact that two linear combinations of the same linearly independent subset are exactly equal if the corresponding coefficients are equal.
Polynomials
Two polynomials
and
are equal if and only if their coefficients match:
example
The two polynomials and are given. For which values of and are the two polynomials equal?
Must apply:
So it is compared:
- (Comparison of the coefficients of )
- (Comparison of the coefficients of )
Solution: and
Trigonometric polynomials
The following are compared:
- (Comparison of the coefficients of )
- (Comparison of the coefficients of )
Solution: ;
See also
literature
- Guido Walz (Ed.): Lexicon of Mathematics . tape 3 (Inp-Mon). Springer Spektrum Verlag, Mannheim 2017, ISBN 978-3-662-53501-1 , p. 131 , doi : 10.1007 / 978-3-662-53502-8 .