Find vector decomposition in basis, online calculator

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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 vector b in the basis formed by linearly independent system of n-dimensional vectors vector a1 , vector a2 , ... , vector an , has the following form:

vector b = λ1 vector a1 + λ2 vector a2 + ... + λn vector an

, where λi − some constants called the coefficients of the decomposition (linear combination) of the vector vector b in basis vector a1 , vector a2 , ... , vector an.

Our online calculator is able to find the decomposition of vector in basis with step by step solution for free.

Decompose vector by basis
Vector A11 by:
Vector A22 by:
Vector B by:
Find vector decompositionb1534in basis:a112a22311243
Vector A11 = { }
Vector A22 = { }
Vector B = { }


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