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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 Checking if estimator is biased
What is an element here? What is the range in n-element sample? And bias depends on the problem (I would suspect more information is needed - an estimator depends on the model and noise).
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 :)