pipebomb

The Kronecker product of an argument X and a 2x2 matrix, increases the dimensions of each argument X individually. If each argument X is a scalar value, it now becomes a 2x2 matrix. How are these arguments now aligned with each other and the other elements in the resultant matrix? For example: In a matrix T, if we have several values and a certain number of 0s like: T= [0 1 0] [0.3 0 0.7] [0.1 0 0] For the new matrix TT, we perform the Kronecker product of the values in the second diagonal (i.e. of 1 and of 0.7) with a 2x2 matrix Q which is Q is [0.8 0.2] [0.4 0.6] and the Kronecker product of the values in the first column (i.e. of 0.3 and of 0.1) with a 2x2 matrix G which is G is [1 1] [1 1] Each value i.e. 1, 0.7, 0.3, 0.1 now results into a 2x2 matrix How are the resultant Kronecker product values aligned into the new resultant matrix TT, since the 0s remain as single scalar vaules? With the dimensions of only a few elements increasing, there will be an alignment issue with regard to the existing unchenanged elements i.e. the 0 values. How do I align them correctly to form a new resultant matrix without losing context? Do I (by default) HAVE to perform Kronecker product with the 0s also? If so, which 2x2 matrix do I use for that (Q or G)? For further reference: This problem arises from trying to validate and repeat the mathematical model given in Equations (19) and (20) to form a new matrix given in Equation (18) in the publication: T. Issariyakul and E. Hossain, "Performance modeling and analysis of a class of ARQ protocols in multi-hop wireless networks, " IEEE Transactions on Wireless Communications, vol. 5, no. 12, Dec. 2006, pp. 3460-3468. Thanks