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CHANGE OF BASES

CHANGE OF BASES. Arbitrary vector spaces are so … i t is not so easy to do any meaningful computa-tion in them. But, as we have seen, if we have a basis f or an arbitrary finite dimensional vector space V , then the coordinate mapping

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CHANGE OF BASES

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  1. CHANGE OF BASES Arbitrary vector spaces are so … it is not so easy to do any meaningful computa-tion in them. But, as we have seen, if we have a basis for an arbitrary finite dimensional vector space V, then the coordinate mapping establishes an isomorphism (one-to-one, onto linear transformation) between V and

  2. Note that

  3. The following picture helps us visualize the situation:

  4. Let’s look at another figure. Note the textbook’s notation, plus the fact that all arrows are isomorphisms. Also note that

  5. Solution. From

  6. For ease we copy the four vectors

  7. Both are non homogeneous systems of two equa-tions in two unknowns, and both require row reducing the matrix to the identity

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