John U
Reputation
Top tag
Next privilege 250 Rep.
 Jan 24 comment An inequality on the root of matrix products (part 2 - the reverse case) Re-asked - looking really for a generic result that really considers the case in which the matrix is never negative definite. Jan 24 comment An inequality on the root of matrix products (part 2 - the reverse case) OK. Thank you.. apologies for the delay in replying to this post - I have been travelling with very little internet access. This is a kind of degenerative situation. I am considering only real matrices and the zero matrix is almost like an indefinite matrix (well it is neither pos-def, neg-def, indef etc by any standard definition). Apologies as the question was a little ambiguous in this regard - though I am really looking for confirmation it is never negative definite as noted also in the question. Jan 15 comment An inequality on the root of matrix products (part 2 - the reverse case) This inequality arises when looking at partitioned covariance matrices $[A,C; C,B]\geq0$. Note $C=A^{1/2}SB^{1/2}$ in such partitions where $I-SS^T\geq0$. Jan 15 awarded Promoter Jan 15 awarded Nice Answer Jan 14 comment Are all small probabilities incomputable? This is a kind of problem-specific question (and particularly suited to finance like situations - though others applications are clearly relevant). He is really saying something like the probability of rare events (like the GFC) cannot be computed accurately using the sample set available because it is too small to have been influenced sufficiently by small probability outcomes. The statement is simply not true as a general matter of principal (he even notes "natural systems" as a counterexample to his own claim). Jan 14 comment An inequality on the root of matrix products (part 2 - the reverse case) The scalar case is "positive definite" for all $s=[-1,1]$ and $a,b>0$. I am really looking for confirmation it is never negative definite (and preferably never negative semi-definite). Jan 14 revised Four Children Combination Problem added 662 characters in body Jan 14 comment Four Children Combination Problem Improved hint: Start by "choosing" two of your own four kids. There are 6 different combinations here. For a particular "choice" of your own kids, now how many choices do I have to pick from on the other side (it is dependent on the first choice but it is reasonably straightforward to see the pattern)? Jan 14 comment Four Children Combination Problem This simplifies things actually. So without even doing anything technical you can just enumerate the numbers (if the same sex is allowed it just adds to the total but not much). Jan 14 answered Four Children Combination Problem Jan 14 comment Eigenvalues and eigenvectors of a matrix. This is a $2\times 2$ rotation matrix.. Eigenvalues/eigenvectors are easy to search for. Jan 14 revised An inequality on the root of matrix products (part 2 - the reverse case) added 26 characters in body Jan 14 comment Splitting a sandwich and not feeling deceived The difficulty of enforcing the ratios depends on the problem I think.. if we think of just a piece of paper and cutting as drawing lines to divide the paper into rectangles (whose area as a percentage of the whole paper represents the division of the wealth of El Dorado to make it interesting) then enforcing the required ratios is just a matter of enforcing lines to be drawn horizontally and vertically (no matter how many people are involved).. Jan 14 revised Splitting a sandwich and not feeling deceived deleted 279 characters in body Jan 14 comment Splitting a sandwich and not feeling deceived Haha.. no.. we could formulate the "edited" part so it works I think for any number of people by constraining the way the subsequent person "cuts" so that some kind of ratios are maintained. Would not be hard to formulate and indeed this has intrigued me. It still might be wrong so I may try and formulate and generalise (its probably known also). Surely there are more ways to solve this problem though - depending on how much you want to mangle the sandwich :). Jan 14 comment Splitting a sandwich and not feeling deceived I know there is the known solution posted in the OP comments - I just feel there should be multiple ways to achieve this and I already started thinking about it :) Jan 14 revised Splitting a sandwich and not feeling deceived added 618 characters in body Jan 14 comment Splitting a sandwich and not feeling deceived Of course if it was an actual sandwich it would be destroyed probably by cutting it into 27 pieces :) Jan 14 answered Splitting a sandwich and not feeling deceived