Change of basis

Common card · No. 233304

In mathematics, an ordered basis of a vector space of finite dimension n allows representing uniquely any element of the vector space by a coordinate vector, which is a finite sequence of n scalars called coordinates. If two different bases are considered, the coordinate vector that represents a vector v on one basis is, in general, different from the coordinate vector that represents v on the other basis. A change of basis consists of converting every assertion expressed in terms of coordinates relative to one basis into an assertion expressed in terms of coordinates relative to the other basis. Such a conversion results from the change-of-basis formula, which expresses the coordinates relative to one basis in terms of the coordinates relative to the other basis. Using matrices, this formula can be written x o l d =...

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