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Unformatted text preview: . Show that ( I ⊗ A )( I ⊗ B ) = ( 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 . Describe an algorithm to evaluate the matrix vector product y = ( A ⊗ B ) x i.e., given A, B, x determine y . What is the complexity of your algorithm and how does it compare to the standard matrixvector product computation? 2...
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 Fall '06
 gallivan
 Linear Algebra, Vector Space, Euclidean vector

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