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Unformatted text preview: B as columns, then we get a matrix P B . As in the example, x = P B [ x ] B . The matrix P B is called the changeofcoordinate matrix from B to the standard basis in R p . The matrix P B is invertible. WHY AND HOW CAN WE USE THIS FACT? THE THINNING FACT, FINALLY. For any vector space V with basis B , the coordinate mapping x → [ x ] B is a onetoone linear transformation from V onto R p . The coordinate mapping makes any vector space with a ﬁnite basis look and act just like R p . This means we can use coordinates to test linear independence and spanning in any vector space. EXAMPLE. Use coordinate vectors to test the linear independence of the polynomials 12 t 23 t 3 , t + t 3 , 1 + 3 t2 t 2 . HOMEWORK: SECTION 4.4...
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This note was uploaded on 04/15/2008 for the course M 340L taught by Professor Pavlovic during the Spring '08 term at University of Texas at Austin.
 Spring '08
 PAVLOVIC
 Linear Algebra, Algebra, Vector Space

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