If $A$ and $B$ are similar, can the same be said of $A^t$ and $B^t$?   $A$ similar to $B$ $\iff \exists P$ such that  $A = PBP^{-1}$  Apply the transpose on both sides  $A^t = (PBP^{-1})^t = (P^{-1})^tB^tP^t = (P^t)^{-1}B^tP^t$  Can I conclude that they are similar?
Prove that, if A and B is similar, then $A^T$ is similar to $B^T$.  Attempt: I try to use the defn of similarity, and then the rule to transpose in different order, but get nowhere. This should be simple...  (Note to self: page 92.)
How to perform two-sample t-tests in R by inputting sample statistics rather than the raw data? Let's say we have the statistics given below  gender mean sd n f 1.666667 0.5773503 3 m 4.500000 0.5773503 4   How do you perform a two-sample t-test (to see if there is a significant difference between the means of men and women in some variable) using statistics like this rather than actual data?  I couldn't find anywhere on the internet how to do this. Most of the tutorials and even the manual deal with the test with the actual data set only. ASP.NET Call Code Behind Function From Javascript I have a filename in a format like:     system-source-yyyymmdd.dat   I'd like to be able to parse out the different bits of the filename using the "-" as a delimiter. Is there any Stack Exchange site where the main topic is literature?  I have tried the English Language site, but it seems that it is not the appropriate site.  Perhaps the writers site would work? But, then again, the main point is different than the one I am searching for. Why is variance squared? The mean absolute deviation is:   $$\dfrac{\sum_{i=1}^{n}|x_i-\bar x|}{n}$$   The variance is: $$\dfrac{\sum_{i=1}^{n}(x_i-\bar x)^2}{n-1}$$   So the mean deviation and the variance are measuring the same thing, yet variance requires squaring the difference. Why? Squaring always gives a non-negative value, but the absolute value is also a non-negative value. Why isn't it $|x_i-\bar x|^2$, then? Squaring just enlarges, why do we need to do this?  A similar question is , but mine is a little different. Thanks. I have an issue with my Minecraft launcher - I downloaded modpack for minecraft then the launcher started an update for the modpack version which it's 1.6.2, however then I started to get the issue      [15:40:59 ERROR]: Gave up trying to download      for job 'Version &amp; Libraries'      [15:40:59 ERROR]: Job 'Version &amp; Libraries' finished with 26   failure(s)! (took 0:01:06.362)   At the same time I had just downloaded Avira antivirus and ran it, but unfortunately  removing it and trying again didn't help. I've tried to restore the system to the point before downloading the antvirus and the mod pack a 2 days ago, I've tried turning off the firewall and I have tried removing the whole .minecraft folder all with no luck at all. I can't figure it out, all the servers are working and I have good internet connection but some of the files download fine and other don't.  The full log is here:  [15:40:59 WARN]: Couldn't download https ://libraries.minecraft.net/net/sf/jopt-simple/jopt-simple/4.5/jopt-simple-4.5.jar for job 'Version &amp; Libraries' java.net.SocketTimeoutException: connect timed out         at java.net.TwoStacksPlainSocketImpl.socketConnect(Native Method) ~[?:1.7.0_45]         at java.net.AbstractPlainSocketImpl.doConnect(Unknown Source) ~[?:1.7.0_45]         at java.net.AbstractPlainSocketImpl.connectToAddress(Unknown Source) ~[?:1.7.0_45]         at java.net.AbstractPlainSocketImpl.connect(Unknown Source) ~[?:1.7.0_45]         at java.net.PlainSocketImpl.connect(Unknown Source) ~[?:1.7.0_45]         at java.net.SocksSocketImpl.connect(Unknown Source) ~[?:1.7.0_45]         at java.net.Socket.connect(Unknown Source) ~[?:1.7.0_45]         at sun.security.ssl.SSLSocketImpl.connect(Unknown Source) ~[?:1.7.0_45]         at sun.net.NetworkClient.doConnect(Unknown Source) ~[?:1.7.0_45]         at sun.net.www.http.HttpClient.openServer(Unknown Source) ~[?:1.7.0_45]         at sun.net.www.http.HttpClient.openServer(Unknown Source) ~[?:1.7.0_45]         at sun.net.www.protocol.https.HttpsClient.&lt;init&gt;(Unknown Source) ~[?:1.7.0_45]         at sun.net.www.protocol.https.HttpsClient.New(Unknown Source) ~[?:1.7.0_45]         at sun.net.www.protocol.https.AbstractDelegateHttpsURLConnection.getNewHttpClient(Unknown Source) ~[?:1.7.0_45]         at sun.net.www.protocol.http.HttpURLConnection.plainConnect(Unknown Source) ~[?:1.7.0_45]         at sun.net.www.protocol.https.AbstractDelegateHttpsURLConnection.connect(Unknown Source) ~[?:1.7.0_45]         at sun.net.www.protocol.http.HttpURLConnection.getInputStream(Unknown Source) ~[?:1.7.0_45]         at java.net.HttpURLConnection.getResponseCode(Unknown Source) ~[?:1.7.0_45]         at sun.net.www.protocol.https.HttpsURLConnectionImpl.getResponseCode(Unknown Source) ~[?:1.7.0_45]         at net.minecraft.launcher.updater.download.ChecksummedDownloadable.download(ChecksummedDownloadable.java:49) ~[launcher.jar:?]         at net.minecraft.launcher.updater.download.DownloadJob.popAndDownload(DownloadJob.java:108) [launcher.jar:?]         at net.minecraft.launcher.updater.download.DownloadJob.access$000(DownloadJob.java:12) [launcher.jar:?]         at net.minecraft.launcher.updater.download.DownloadJob$1.run(DownloadJob.java:89) [launcher.jar:?]         at java.util.concurrent.Executors$RunnableAdapter.call(Unknown Source) [?:1.7.0_45]         at java.util.concurrent.FutureTask.run(Unknown Source) [?:1.7.0_45]         at java.util.concurrent.ThreadPoolExecutor.runWorker(Unknown Source) [?:1.7.0_45]         at java.util.concurrent.ThreadPoolExecutor$Worker.run(Unknown Source) [?:1.7.0_45]         at java.lang.Thread.run(Unknown Source) [?:1.7.0_45] [15:40:59 ERROR]: Gave up trying to download https ://libraries.minecraft.net/net/sf/jopt-simple/jopt-simple/4.5/jopt-simple-4.5.jar for job 'Version &amp; Libraries' [15:40:59 ERROR]: Job 'Version &amp; Libraries' finished with 26 failure(s)! 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Virtual member call in a constructor Does the sum of reciprocals of primes converge? Is this series known to converge, and if so, what does it converge to (if known)?  Where $p_n$ is prime number $n$, and $p_1 = 2$,  $$\sum\limits_{n=1}^\infty \frac{1}{p_n}$$ Google chrome is reading characters backwards How to get selected text from textbox control with javascript What is crop factor and how does it relate to focal length? I'm reading through  for the , which contains this figure on page 16:    This is of course an instrumentation amplifier that apparently uses an inverting amplifier's output instead of a ground in the lower-right corner of the above figure, but what really perplexes me is the 100 k&Omega; resistors attached directly to the noninverting inputs of three of the four amps. I don't recall seeing an instrumentation amplifier circuit in books or application notes that have them, and all of the instrumentation amplifiers I've built using the three op-amp scheme works fine without them.  The datasheets specifies an input resistance of 1012 &Omega;, which is 10,000,000 times greater than 100 k&Omega;, so it doesn't seem to add anything to the already high-impedance JFET inputs. I thought perhaps it has something to do with input bias currents, but that's just me making a wild stab in the dark.  Curiously, figure 26 in the same datasheet (page 18) shows a two-op-amp version of an instrumentation amplifier without the 100 k&Omega; resistors at the noninverting op-amp inputs!  What's the purpose of the 100 k&Omega; resistors at the noninverting inputs in the above circuit? Am I missing something completely obvious? Subdivision Surface on curved mesh I'm trying to delete those ugly lines visible in the cylindrical shape of the lens. What is causing them is the added edge loops I made for the protruding detail with the switch. The problem is that if I delete those edges, it'll look even worse because of the n-gons. Any ideas? How to configure logback to skip logging messages from org.package.* with all levels below WARN?