ChangeofBasisMatrix
A changeofBasisMatrix, in linear algebra, is an invertible matrix used to translate coordinate representations of vectors from one basis to another. Given two ordered bases B = (b1, ..., bn) and C = (c1, ..., cn) for a finite-dimensional vector space V, the change-of-basis matrix from B to C, denoted P_{C<-B}, satisfies [v]_C = P_{C<-B} [v]_B for every vector v in V. Here [v]_B and [v]_C denote the coordinate column vectors of v with respect to bases B and C, respectively.
Construction and interpretation: To form P_{C<-B}, express each vector in B as a linear combination of the
Applications and examples: The change-of-basis matrix is used to convert representations of vectors when switching bases,