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Unformatted text preview: by O ( n ). (a) Show that A1 = A t for all A O ( n ). (b) Show that A t O ( n ) for all A O ( n ). (c) Show that AB O ( n ) for all A,B O ( n ). (3) Let L : R 3 M (3) be the linear map dened by L ( x i + y j + z k )) = z yz xyx Observe that the image of L is the space A (3) of 3 3, skewsymmetric matrices. Show that L ( u v ) = [ L ( u ) ,L ( v )] where [ A,B ] denotes the Lie bracket of A and B , i.e. [ A,B ] = ABBA . 1...
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This note was uploaded on 10/12/2009 for the course MATH 136 taught by Professor Staff during the Spring '08 term at University of Washington.
 Spring '08
 Staff
 Matrices, Vector Space, Complex Numbers

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