Criteria for the difference of two matrices to be positive semidefinite when the eigenvectors are known
Under what conditions is the difference between a rank $1$, postive semidefinite matrix and a hermitian matrix positive semidefinite?
When clicking &quot;edit&quot; I see:  Your edit will be placed in a queue until it is peer reviewed. We welcome edits that make the post easier to understand and more valuable for readers. Because community members review edits, please try to make the post substantially better than how you found it, for example, by fixing grammar or adding additional resources and hyperlinks.  Like:     Likewise, when I am not logged in, clicking &quot;improve this question&quot; or &quot;improve this answer&quot; shows:  You are not . Your edit will be placed in a queue until it is .  And when I click 'Save', I get:  Thanks for submitting an edit. It is only visible to you until it's been approved by trusted community members  Like:     Who can suggest an edit? Where do suggested edits go? Who can vote on a suggested edit? How do suggested edits get reviewed? Can I earn reputation? What about abuse or bad edits? Sometimes the Community user approves or rejects my edit. Why is that? When can I not suggest an edit? Is there a minimum change requirement for a suggested edit? How do I check my suggested edit history? I disagree with the reasons why my suggested edit was rejected. What can I do? How do I know whether there are edits waiting for review? Someone suggested an edit to my own post, and the reviewers took the wrong action. What can I do? Are tag wikis included in this scheme? What do the &quot;Improve Edit&quot; and &quot;Reject and Edit&quot; buttons do? Why are apparently valid links to rejected edits resulting in 404 errors?   For more information about editing, see &quot;&quot; in the . Is there anyway to find and remove ligatures from tex file? Sometimes when I copy/paste a text to Winedt, it shows perfect, but when I compile it to Pdf, some issues appear, e.g. finding becomes nding.  I am wondering if there is any way to search and find these characters?  Here is an example file (needs utf8 encoding).  \documentclass{article} \begin{document} ﬁ \end{document} Code: \documentclass[12pt]{article} \usepackage{pgfplots} \usepackage{float} \pgfplotsset{compat=1.17} \usepackage{tikz} \usetikzlibrary{shapes, arrows.meta, automata, positioning, matrix, calc} \usepackage[RPvoltages, american,siunitx]{circuitikz} \usepackage[margin=1in]{geometry}  \usepackage{steinmetz} \begin{document}         \begin{figure}[H]         \centering         \begin{circuitikz}             \draw(0,0) to[V = $\vec{V}_g$] ++(0, 3) to[R = 50 &lt;\ohm&gt;] ++(3, 0) to[C = 1&lt;\micro\farad&gt;, v = $\vec{V}_o$] ++(0, -3) to[short] ++(-3, 0);         \end{circuitikz}     \end{figure} \end{document}  Output:  As we can see, $\vec{V}_o$ is almost touching the capacitor. How to adjust the spacing for the voltage label? Actually, can  potentially solve the problem? Note that what I am trying to draw is based off of this: How can I grep in PDF files? Is there a way to search PDF files using grep, without converting to text first in Ubuntu? Can I use virtualbox with a 64 Bit image in a 32 bit host I have Virtualbox 4.1.20 in Ubuntu 12.04 32 Bit (With PAE) and I want to run Ubuntu Server 64 Bit on the Guest. Is this possible?. I ask since I get the following warning:    I want to make sure that there is no option to "emulate" this. I have a 64 bit CPU that supports virtualization. The Intel DZ68DB motherboard with an Intel I7 2600 CPU. I am interested in finding out how confident my model (say Logistic Regression) is in predicting the label of a new data point. For example, if it is not confident, I better abstain from making a prediction.   Logistic Regression outputs probabilities, which gives you a notion that there is confidence in prediction. But in fact, it is not. $P(y|x)$ being 0.3, doesn't tell me that the model is confident in its prediction or not. All, we can say is that it believes 100% that class A is 0.3 and other class is 0.7.  Can we use confidence intervals of LR as some sort of confidence in prediction? E.g., larger the difference between upper and lower bound for a particular data point, less confident it is, and vice-versa?  If not, how can we build confidence in our prediction? Can anybody guide me to some paper or field of study? Is there a "theirs" version of "git merge -s ours"? When merging topic branch "B" into "A" using git merge, I get some conflicts. I know all the conflicts can be solved using the version in "B".  I am aware of git merge -s ours. But what I want is something like git merge -s theirs.   Why doesn't it exist? How can I achieve the same result after the conflicting merge with existing git commands? (git checkout every unmerged file from B)  UPDATE: The "solution" of just discarding anything from branch A (the merge commit point to B version of the tree) is not what I am looking for. What is the advantage to crushed garlic over minced garlic beyond texture? I use a lot of garlic in my cooking, especially minced garlic.  But lately I've been doing some more recipes with crushed garlic and while I love the texture of cooked garlic, I can't see how it could be better than minced garlic for the overall taste.  Is there an advantage to crushed garlic over minced garlic, beyond texture? How can I maximize the "blurry background, sharp subject" (bokeh) effect? Can someone give me an example for this question on reflexivity please. How is this reflexive? Can you show an example with numbers from the set?     Question 6   Let $X = \{0,1,2,3,\dotsc, 9\}$. Define a relation $\mathcal R$ from $X$ by "$x$ is related to $y$ if $x$ and $y$ gives the same remainder on division by $3$".   (a) Show that $\mathcal R$ is an equivalence relation.   Anwser:   (a) $\mathcal R$ is clearly both reflexive and symmetric, for every number has the same (unique) remainder on division by $3$ as itself and if $a$ has the same remainder on division by $3$ as does $b$, then $b$ has the same remainder on division by $3$ as $a$ also. Similarly $\mathcal R$ is transitive, for if $a\mathcal R b$ and $b\mathcal R c$, then $a$, $b$, and $c$ all have the same remainder on division by $3$, so $a\mathcal R c$ also. This is a comic book I read no later than 1993 (so is pre-1993).  And probably after 1988 though I can't be certain.  The protagonist is a huge barbarian with an axe, who seems like an old man, who is defending a series of gigantic walls against an invading army, apparently single-handedly. They keep having to fall back to inner walls. He has to get a massage at one point (not that kind of comic btw).  It's not a super-hero or funny comic, it's more of a serious graphic novel.  That's about it, sorry it's so vague. Why does find -mtime +1 only return files older than 2 days? I'm struggling to wrap my mind around why the find interprets file modification times the way it does.  Specifically, I don't understand why the -mtime +1 doesn't show files less than 48 hours old.   As an example test I created three test files with different modified dates:   [root@foobox findtest]# ls -l total 0 -rw-r--r-- 1 root root 0 Sep 25 08:44 foo1 -rw-r--r-- 1 root root 0 Sep 24 08:14 foo2 -rw-r--r-- 1 root root 0 Sep 23 08:14 foo3   I then ran find with the -mtime +1 switch and got the following output:  [root@foobox findtest]# find -mtime +1 ./foo3   I then ran find with the -mmin +1440 and got the following output:   [root@foobox findtest]# find -mmin +1440 ./foo3 ./foo2   As per the man page for find, I understand that this is expected behavior:   -mtime n         File’s  data was last modified n*24 hours ago.  See the comments         for -atime to understand how rounding affects the interpretation         of file modification times.   -atime n        File  was  last  accessed n*24 hours ago.  When find figures out        how many 24-hour periods ago the file  was  last  accessed,  any        fractional part is ignored, so to match -atime +1, a file has to        have been accessed at least two days ago.   This still doesn't make sense to me though.  So if a file is 1 day, 23 hours, 59 minutes, and 59 seconds old, find -mtime +1 ignores all that and just treats it like it's 1 day, 0 hours, 0 minutes, and 0 seconds old?  In which case, it's not technically older that 1 day and ignored?   Does... not... compute. I occasionally update my kernel from this web site    I have been always downloading 3 deb files for installing  linux header all, linux image and linux headers. I noticed one more deb file recently for 64 bit kernel called Linux-image-extra.  I would like to know what does kernel file Linux-image-extra do and should I also install it? Javascript to check whether a checkbox is being checked or unchecked Inheriting Options? Index entries duplicated for captions Present-perfect-tense vs. Simple-past-tense Zip all files in directory? Is there a way to zip all files in a given directory with the zip command? I've heard of using *.*, but I want it to work for extensionless files, too. Saving high-quality graphics through commands Can high level Eldritch blast be used with War Caster?