- #1
perplexabot
Gold Member
- 329
- 5
Hey all. So I have been reading this article and have a question I would like to ask. I will be referring to this article extensively so it would be kind of you to open it: http://www.ee.ucr.edu/~yhua/MILCOM_2013_Reprint.pdf
I believe reading the article is not required to answer my questions (i did personally read it tho up until where I am stuck), but I will refer to the equation numbers in the article instead of typing them out here.
So, on page 5 of the pdf, there is a matrix, G2, or equation number (22). I am basically trying to figure out how they constructed this matrix! Specifically the left two partitions.
I believe reading the article is not required to answer my questions (i did personally read it tho up until where I am stuck), but I will refer to the equation numbers in the article instead of typing them out here.
So, on page 5 of the pdf, there is a matrix, G2, or equation number (22). I am basically trying to figure out how they constructed this matrix! Specifically the left two partitions.
- Equation (15) gives the definition of G, and shows that G depends on u(k).
- Equation (12) defines u(k) to be [u1T | u2T | ##\bar{g}## T | 1].
- The two lines after equation (12) define u1T and u2T
- Equation (5) defines ##\bar{g}## T, giT, and grT
- Now that we have all the definitions stated we can go back to equation (22), or G2. It is stated in the two lines above equation (22) that m = 2 (m is the column size of ##\bar{g}## T). Right?
- Now if ##\bar{g}## T contains only two elements that means, according to equation (5), giT, and grT would be scalars, right?
- Continuing with this logic and going to the definition of u2T, the difference of the Kronecker product of two scalars, would be zero! would it not? Hence, u2T = 0
- According to the previous bullet point, this would make the second column/partition (from the left) of equation (22) equal to 0, which contradicts what is shown in equation (22)
- Doing the same with u1T and the first column/partition (from the left) of equation (22) would also yield a different answer.