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Unformatted text preview: I ⊗ AB ) 2.3.b . Show that ( A ⊗ I )( I ⊗ B ) = ( I ⊗ B )( A ⊗ I ) = ( A ⊗ B ) 2.3.c . Show that ( A ⊗ I )( B ⊗ I ) = ( AB ⊗ I ) 2.3.d . Show that ( A ⊗ B )( C ⊗ D ) = ( AC ) ⊗ ( BD ) . 2.3.e . Show that if A ∈ C n × n and B ∈ C n × n have inverses A1 and B1 , respectively, then ( A ⊗ B ) has an inverse. 1 Problem 2.4 Let A ∈ C m × m , B ∈ C n × n , x ∈ C mn , and y ∈ C mn . 2.4.a . Describe an algorithm to evaluate the matrix vector product y = ( A ⊗ B ) x i.e., given A, B, x determine y . 2.4.b . What is the complexity of the algorithm? 2.4.c . How does the complexity of the algorithm compare to the standard matrixvector product computation? 2...
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 Fall '06
 gallivan
 Linear Algebra, Vector Space, Euclidean vector, matrixvector product computation

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