Three Dimensions
For example, be a new basis given by its Euler angles. The matrix of the basis will have as columns the components of each vector. Therefore, this matrix will be (See Euler angles article):
Again, any vector of the space can be changed to this new basis by left-multiplying its components by the inverse of this matrix.
Read more about this topic: Change Of Basis, Change of Coordinates of A Vector
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—Thomas Jefferson (17431826)
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