Determinant of a decomplexified matrix Let A be an $n \times n$ matrix with complex entries $$z_{ij} = a_{ij} + I*b_{ij}$$ If AR is its $2n \times 2n$ decomplexified matrix, i. e. the matrix with entries $a_{ij},b_{ij}$  Is it possible to compute det(AR) from det(A) or viceversa?
Determinant of an $n\times n$ complex matrix as an $2n\times 2n$ real determinant If $A$ is an $n\times n$ complex matrix. Is it possible to write $\vert \det A\vert^2$ as a $2n\times 2n$ matrix with blocks containing the real and imaginary parts of $A$?  I remember seeing such a formula, but can not remember where. Any details, (and possibly references) for such a result would be greatly appreciated.
How does the admissions process work for Ph.D. programs in the US, particularly for weak or borderline students? When applying to a PhD program in the US, how does the admissions process work? If an applicant is weak in a particular area, is it possible to offset that by being strong in a different area?  Note that this question originated from this . Please feel free to edit the question to improve it. How to escape '$' and '#' in Facelets/EL? How do I wrap a macro definition in an environment? Show that the free group on $n$ generators is a finite index subgroup of $F_2$ Using covering spaces, prove that for each integer $n \geq 2$, $F_n$ is a finite index subgroup of $F_2$, where $F_n$ is the free group on $n$ generators.  I get how the cayley graph of $F_n$ would be a wedge of $k$ circles and the cayley graph of $F_2$ would be a graph of a vertex and two edges, but I don't understand how we can create an injective map from $F_n$ to $F_2$ and show its a subgroup. (1, eval)('this') vs eval('this') in JavaScript? Why not perma-ban instead of suspend an account for 275 years? I know there are a lot of questions about very long suspension periods, but I came across a case that is quite perplexing. This user had many offenses to earn his long ban, despite being a very prolific and high-rep user with many valuable posts, but the suspension period assigned strains the definition of "suspension."     This account is temporarily suspended network-wide. The suspension   period ends on Mar 18 '(22)92 at 16:28.   I can see why you might want to suspend an account for several years, maybe even a decade, if you don't believe behavior will change. However, what is the point of "suspending" an account for 275 years? Is there a reason why you can't just make it a permanent ban instead of pretending it is a suspension?    On a tangential note, isn't the "temporary" in "temporary suspension" redundant?  Suspend: temporarily prevent from continuing or being in force or effect. I would like my Dock to show only the windows of the current workspace. Especially in the little preview window. I find it very confusing to jump around workspaces when trying to find the right window. Down vote changed to up vote caused reputation meter to pass daily maximum Any thoughts on how one might clear the Android Marketplace search history? For instance, if I recently searched for an android app in the marketplace, the marketplace search maintains a history list of which apps/keywords that I have recently looked for.    Thanks in advance! Proof that the largest eigenvalue of a stochastic matrix is $1$ What are the rules for animal mating? Is  structured data (in Microdata, JSON-LD, or RDFa) relevant for SEO?   I know that structured data can provide benefits in other areas, but here I’m only asking about its significance for general web search engines. Prove or disprove that $f(x) = \sin x/x$ is uniformly continuous over the interval $(0,1)$? I am thinking of $\lim_{x \to 0} \ {f(x)} = 1$ but I am confused as $x=0$ is not in the domain and also I want to write an $\epsilon$-$\delta$ proof. So any help is much appreciated!  Thanks! "named" vs "that is named" How to set the monitor to its native resolution which is not listed in the resolutions list? After installing Ubuntu 10.04 with my Samsung SyncMaster B2030, native resolution (1600X900) is not found in the list of resolutions. How can I install the latest Netbeans? In Ubuntu Software Center the Netbeans version is netbeans 7.0.1+dfsg1-5ubuntu2 but Netbeans 8.1 is available in the Netbeans website. What spell targets count for the Graviturgy Magic wizard's Gravity Well feature? The  feature from the  (EGtW, p. 185) triggers &quot;whenever you cast a spell on a creature&quot;, and has an effect &quot;if the target is willing to move, the spell hits it with an attack, or it fails a saving throw against the spell.&quot; It's not clear to me what kinds of spells can actually trigger this feature. Based on the singular phrasing of &quot;on a creature&quot; and the later use of the word &quot;target&quot;, I would normally read this as only applying to spells that explicitly target creatures (and perhaps only those with a single target, in contrast to the phrasing of the  feature of the  wizard, for example). However, spells that target a location can use the word target in a different sense (see ). What's actually going on here? Does this feature only work on targeted spells? Or does it function for area of effect spells as well? Or is this just an ambiguous phrasing that will rely on the DM's ruling? Extract date from a variable in a different format Let me explain you the problem   $ date +%c -d "$d" Tue 31 Dec 2013 01:13:06 PM CET $ date +'Today is %F' -d "$d" Today is 2013-12-31   This solution corresponds to current date.  But I have one variable which stores date other than current date  $Prev_date="Wed Dec 25 06:35:02 EST 2013"    I am looking for solution to read this date as 2013-12-25 and store it in a variable.  I have tried this:  a=`date --date=$Prev_date '+%y/%m/d'` echo $a   It's giving this error:  date: illegal option -- date=Wed usage: date [-u] mmddHHMM[[cc]yy][.SS] date [-u] [+format] date -a [-]sss[.fff] View linked Excel 'Windows' on separate screens If the Universe is expanding, how is that galaxies run into each other? As the title says. If everything is moving outward, thrown by the Big Bang, how could two Galaxies end up with velocity vectors that run them into each other?