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Unformatted text preview: Chapter 3. Vector Spaces Math1111 Change of Basis Change Coordinates  Further Example 2 Example . Let E , F , H be ordered bases for R n . Suppose S = the transition matrix from F to E , T = the transition matrix from H to F . Find the transition matrix from H to E . Chapter 3. Vector Spaces Math1111 Change of Basis Change Coordinates  Further Example 2 Example . Let E , F , H be ordered bases for R n . Suppose S = the transition matrix from F to E , T = the transition matrix from H to F . Find the transition matrix from H to E . Ans . Let v ∈ R n . Suppose x = ( x 1 ··· x n ) T , y = ( y 1 ··· y n ) T , z = ( z 1 ··· z n ) T be the coordinate vectors of v w.r.t. E , F , H respectively. Chapter 3. Vector Spaces Math1111 Change of Basis Change Coordinates  Further Example 2 Example . Let E , F , H be ordered bases for R n . Suppose S = the transition matrix from F to E , T = the transition matrix from H to F . Find the transition matrix from H to E . Ans . Let v ∈ R n . Suppose x = ( x 1 ··· x n ) T , y = ( y 1 ··· y n ) T , z = ( z 1 ··· z n ) T be the coordinate vectors of v w.r.t. E , F , H respectively. Then, x = S y and y = T z . Hence, x = ST z . i.e. ST is the transition matrix from H to E . Chapter 3. Vector Spaces Math1111 Change of Basis Change Coordinates  Further Example 2 Example . Let E , F , H be ordered bases for R n . Suppose S = the transition matrix from F to E , T = the transition matrix from H to F . Find the transition matrix from H to E . Ans . Let v ∈ R n . Suppose x = ( x 1 ··· x n ) T , y = ( y 1 ··· y n ) T , z = ( z 1 ··· z n ) T be the coordinate vectors of v w.r.t. E , F , H respectively. Then, x = S y and y = T z . Hence, x = ST z . i.e. ST is the transition matrix from H to E . Summary: Chapter 3. Vector Spaces Math1111 Change of Basis Change Coordinates  Further Example 2 Example . Let E , F , H be ordered bases for R n . Suppose S = the transition matrix from F to E , T = the transition matrix from H to F . Find the transition matrix from H to E . Ans . Let v ∈ R n . Suppose x = ( x 1 ··· x n ) T , y = ( y 1 ··· y n ) T , z = ( z 1 ··· z n ) T be the coordinate vectors of v w.r.t. E , F , H respectively. Then, x = S y and y = T z . Hence, x = ST z . i.e. ST is the transition matrix from H to E . Summary: Chapter 3. Vector Spaces Math1111 Change of Basis Change Coordinates  Further Example 2 Example . Let E , F , H be ordered bases for R n . Suppose S = the transition matrix from F to E , T = the transition matrix from H to F . Find the transition matrix from H to E . Ans . Let v ∈ R n . Suppose x = ( x 1 ··· x n ) T , y = ( y 1 ··· y n ) T , z = ( z 1 ··· z n ) T be the coordinate vectors of v w.r.t. E , F , H respectively....
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This note was uploaded on 04/30/2010 for the course MATH 1111 taught by Professor Dr,li during the Spring '10 term at HKU.
 Spring '10
 Dr,Li
 Math, Vector Space

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