Lecture-2 - Preliminaries Lecture-2 Eigen Vectors and Eigen...

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1 Preliminaries Lecture-2 Eigen Vectors and Eigen Values The eigen vector, x, of a matrix A is a special vector, with the following property x Ax l = Where ë is called eigen value 0 ) det( = - I A l To find eigen values of a matrix A first find the roots of: Then solve the following linear system for each eigen value to find corresponding eigen vector 0 ) ( = - x I A l
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2 Example - = 7 0 0 4 3 0 0 2 1 A 1 , 3 , 7 3 2 1 - = = = l l l = = = 0 0 1 , 0 2 1 , 4 4 1 3 2 1 x x x Eigen Values Eigen Vectors Eigen Values 0 ) det( = - I A l 0 ) 1 0 0 0 1 0 0 0 1 7 0 0 4 3 0 0 2 1 det( = - - l 0 ) 7 0 0 4 3 0 0 2 1 det( = - - - - l l l 7 3, , 1 0 ) 7 )( 3 )( 1 ( 0 ) 0 ) 7 )( 3 )(( 1 ( = = - = = - - - - = - - - - - l l l l l l l l l
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Eigen Vectors 0 ) ( = - x I A l = + - 0 0 0 ) 1 0 0 0 1 0 0 0 1 7 0 0 4 3 0 0 2 1 ( 3 2 1 x x x = 0 0 0 8 0 0 4 4 0 0 2 0 3 2 1 x x x 0 , 0 , 1 0 8 0 0 0 4 4 0 0 0 2 0 3 2 1 3 3 2 2 = = = = + + = + + = + + x x x x x x x = 0 0 1 1 x 1 - = l = = n i ii A A trace 1 ) ( 1 det det orthogonal is , 1 ± = = = = = - T T T T Q Q Q Q Q I Q Q QQ es eigen valu are
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This note was uploaded on 06/12/2011 for the course COT 6505 taught by Professor Shah during the Spring '07 term at University of Central Florida.

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Lecture-2 - Preliminaries Lecture-2 Eigen Vectors and Eigen...

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