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Mathematics-Online course: Linear Algebra - Matrices - Linear Maps

Coordinate Transformation under Change of Basis

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Changing the basis $ E\to E'$ the coordinates of a given vector $ v$ change according to

$\displaystyle v_E = A v_{E'},\, $

where the columns of matrix $ A$ contain the coefficients of basis vectors $ e'_i$ relative to basis $ E$:

$\displaystyle e'_i = \sum_j a_{j,i} e_j\, . $

(Authors: Burkhardt/Höllig/Hörner)
  automatically generated 4/21/2005