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Unformatted text preview: which is linearly dependant. { } is linearly independant. 1.6.22 The condition is that W 1 W 2 , thus we must prove that dim( W 1 W 2 ) = dim( W 1 ) if and only if W 1 W 2 . Let dim( W 1 W 2 ) = dim( W 1 ). As W 1 W 2 W 1 , we see that our assumption gives that W 1 W 2 = W 1 . Thus W 1 = W 1 W 2 W 2 . Conversely let W 1 W 2 . Thus W 1 W 2 = W 1 giving that dim( W 1 W 2 ) = dim( W 1 )....
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This note was uploaded on 02/02/2012 for the course MATH 115A 262398211 taught by Professor Fuckhead during the Spring '10 term at UCLA.
 Spring '10
 FUCKHEAD

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