Arbitrary vector of any -dimensional space can be expressed in the form of the linear combination of some basis vectors of this -dimensional space. Such the decomposition is uniquely one.
Decomposition of the arbitrary -dimensional vector in the basis formed by linearly independent system of -dimensional vectors 1 , 2 , ... , n , has the following form:
= λ1 1 + λ2 2 + ... + λn n
, where λi − some constants called the coefficients of the decomposition (linear combination) of the vector in basis 1 , 2 , ... , n.
Our online calculator is able to find the decomposition of vector in basis with step by step solution.