Vector decomposition

Vector decomposition is the decomposition of a vector of Rⁿ into several vectors, all linearly independent (in mutually distinct directions in the n-dimensional space).

In two dimensions, a vector can be decomposed in many ways. In the Cartesian coordinate system, the vector is decomposed into a portion along the ${\displaystyle {\hat {x}}}$ or ${\displaystyle {\hat {i}}}$ and the ${\displaystyle {\hat {y}}}$ or ${\displaystyle {\hat {j}}}$ directions.

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