Equating coefficients

The coefficient comparison, a method for comparing a linear combination of linearly independent elements of a vector space. Frequently, the vector space of polynomials of degree, such as in the application of the coefficient comparison on the partial fraction is. One uses here the fact that two linear combinations ( of the same elements ) are then equal exactly when their respective coefficients are equal.

Most Comparing two linear combinations of which an unknown and the other known coefficient, to determine the unknown coefficients of the former, which leads to a linear system of equations.

Polynomials

Two polynomials

And

Are equal if their coefficients coincide:

Example

There are given two polynomials and. For which values ​​of and the two polynomials are equal?

Are compared:

Solution: and

Trigonometric polynomials

Are compared:

Solution:;

• Linear Algebra