On Chrome's settings page, chrome://settings, when I go to Search Engine -> Manage search engines chrome://settings/searchEngines and edit stuff in "Other search engines", where are those settings stored? They're synced to my account, but can I download them and import them from another Chrome user/share them with other people?
I have created some search entries in Google Chrome using 'Edit search engines'.  How can I share some of these entries with my colleagues?
I've read a lot about PCA, including various tutorials and questions (such as , , , and ).   The geometric problem that PCA is trying to optimize is clear to me: PCA tries to find the first principal component by minimizing the reconstruction (projection) error, which simultaneously maximizes the variance of the projected data.    When I first read that, I immediately thought of something like linear regression; maybe you can solve it using gradient descent if needed.  However, then my mind was blown when I read that the optimization problem is solved by using linear algebra and finding eigenvectors and eigenvalues. I simply do not understand how this use of linear algebra comes into play.  So my question is: How can PCA turn from a geometric optimization problem to a linear algebra problem? Can someone provide an intuitive explanation?  I am not looking for an answer like  that says "When you solve the mathematical problem of PCA, it ends up being equivalent to finding the eigenvalues and eigenvectors of the covariance matrix." Please explain why eigenvectors come out to be the principal components and why the eigenvalues come out to be variance of the data projected onto them  I am a software engineer and not a mathematician, by the way.  Note: the figure above was taken and modified from . Example of a ring with an infinite inclusion chain of ideals I'm trying to track down an example of a ring in which there exists an infinite chain of ideals under inclusion. (i.e. $I_1 \subsetneq I_2 \subsetneq I_3 \subsetneq...$) How to install apps which require a newer version of iOS on a 1st gen. iPad? I'm trying to solve the following problem:  Given two CRHF $H_1:2^{4n}\to2^{2n}$, $H_2:2^{2n}\to 2^n$, construct the following hash function $H^{*}=H_2(H_1(x))$ compressing from $2^{4n}\to 2^n$. We want to demonstrate that if $H_1$ and $H_2$ are collision resistant then $H^*$ must be collision resistant too.  I made the following reduction  However I'm still unsure on how to calculate ”BAD event” in which $A^{H^∗}$ outputs a collision for $H_{s_1}$, in this case $x^∗=x′$ and the second part of the reduction doesn’t work. I know it is so weird, but last night I set an image on my desktop background and delete the image, then I right-click on the desktop and press the desktop properties to change the style of background (center, stretch and etc) then the desktop properties stopped something like hanging on Windows.   Then a black window alerted something and I press yes without reading it. after that with right-click on the desktop I just see this:    Even some system applications don't work now. for example, I cannot take a screenshot.  Also, my pcmanfm-qt is dead completely, with the command line or clicking on the icon nothing happens.  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