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Unformatted text preview: AB = ± A 1 B A 2 B ² . (8) CaseII The second formula comes from decomposing B = ( B 1 ,B 2 ) where B 1 = ( b 1 , ··· , b t ) (9) B 2 = ( b t + 1 , ··· , b r ) (10) are n × t and n × ( rt ) matrices respectively. Thus we can form the products AB 1 and AB 2 and the second block multiplication formula is AB = ( AB 1 AB 2 ) . (11) CaseIII The last case comes from decomposing A = ± A 1 A 2 ² (12) where A 1 is m × s and A 2 is m × ( ns ) and A = ( B 1 B 2 ) (13) with B 1 and s × r and B 2 an ( ns ) × r matrix respectively. Notice we can form the matrix products A 1 B 1 and A 2 B 2 Then we have the third block multiplication formula AB = A 1 B 1 + A 2 B 2 . (14) 2...
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This note was uploaded on 01/27/2010 for the course MATH 2j taught by Professor Staff during the Winter '08 term at UC Irvine.
 Winter '08
 staff
 Math

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