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# P2 - Here a ij B 1 ≤ i ≤ m 1 ≤ j ≤ n is a...

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University of Central Florida School of Electrical Engineering and Computer Science EGN-3420 - Engineering Analysis. Fall 2009 - dcm Project 2 due Thursday week 9 (100 points) In this project you are asked to write a library for tensor operations. The tensor product of an m × n matrix and a p × q matrix is an mp × nq matrix. For example, if A is an m × n matrix and B is a p × q matrix then, using the Kronecker product representation for the tensor product, we have A B = a 11 B a 12 B . . . a 1 n B a 21 B a 22 B . . . a 2 n B a 31 B a 32 B . . . a 3 n B . . . . . . . . . a m 1 B a m 2 B . . . a mn B with A = a 11 a 12 . . . a 1 n a 21 a 22 . . . a 2 n a 31 a 32 . . . a 3 n . . . . . . . . . a m 1 a m 2 . . . a mn B = b 11 b 12 . . . b 1 q b 21 b 22 . . . b 2 q b 31 b 32 . . . b 3 q . . . . . . . . . b p 1 b p 2 . . . b pq
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Unformatted text preview: . Here, a ij B, 1 ≤ i ≤ m, 1 ≤ j ≤ n is a sub-matrix whose entries are the products of a ij and all the elements of matrix B . The tensor product of two vectors, one of dimension p , and the other of dimension q is a vector of dimension pq . For example, the tensor product of two-dimensional vectors ( a,b ) t and ( c,d ) t is the four-dimensional vector: ± a b ¶ ⊗ ± c d ¶ = ac ad bc bd . The tensor product of two vectors ± 1 ¶ and ± 1 ¶ is: ± 1 ¶ ⊗ ± 1 ¶ = 1 ....
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