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.