Basis Transformation Matrix
Let B and C be two different bases of a vector space V, and let us mark with the matrix which has columns consisting of the C representation of basis vectors b1, b2, ..., bn:
This matrix is referred to as the basis transformation matrix from B to C, and can be used for transforming any vector v from a B representation to a C representation, according to the following theorem:
If E is the standard basis, the transformation from B to E can be represented with the following simplified notation:
where
- and
Read more about this topic: Coordinate Vector
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