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In this post, I want to delve further into sorting. In a question on or.stackexchange.com [1], the subject was minimizing the number of swaps in sorting algorithms. A swap, i.e., an interchange of two items, is a basic operation in sorting. We usually don't pay much attention to this. First, we assume swaps are cheap. If they are not, we can sort not the real data (which can be ...
From [1]:
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When using \({\bf diag}(x)\) in a text, there is always the nagging feeling that there must be a nice way to express this in standard matrix algebra (i.e., some combination of identity matrices, all-ones vectors, and standard matrix multiplications). To remind ourselves, the \({\bf diag}(x)\) function creates a diagonal matrix with \(x_i\) as diagonal elements: \[{\bf diag}(x) =...
