# Find vector decompisition in basis, online calculator

Arbitrary vector of any n-dimensional space can be expressed in the
form of the linear combination of some basis vectors of this n-dimensional
space. Such the *decomposition* is uniquely one.

*Decomposition* of the arbitrary n-dimensional vector
in the basis formed by linearly independent system of n-dimensional vectors
_{1} ,
_{2} , ... ,
_{n} ,
has the following form:

=
λ_{1}
_{1} +
λ_{2}
_{2} + ... +
λ_{n}
_{n}

, where λ_{i} − 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 for free.