I have figured out a possible solution and I only need someone to tell me if I'm correct. The solution is the following:  If a matrix has linearly independent columns, then  $A^+$ = $(A^TA)^{-1}A^T$  Therefore, by operating: = $A^{-1}(A^T)^{-1}A^T$ = $A^{-1}$ since $(A^T)^{-1}A^T = I$ So $A^+ = A^{-1}$  Am I right with this proof?   Thank you
If a matrix has orthonormal columns, they must be linearly independent, so $A^+ = (A^T A)^{−1} A^T$ . Also, the fact that its columns are orthonormal gives $A^T A = I$. Therefore,  $$A^+ = (A^T A)^{−1} A^T = (I)^{-1}A^T = A^T$$  Thus, $A^+ = A^T$. Am I correct? Thank you.
Can I use a one time pad key twice with random plaintext? How to auto close LWC quick action from JavaScript? Looking for a book series about a girl and her friends captured and sold as slaves Split string containing command-line parameters into string[] in C# I have a single string that contains the command-line parameters to be passed to another executable and I need to extract the string[] containing the individual parameters in the same way that C# would if the commands had been specified on the command-line. The string[] will be used when executing another assemblies entry-point via reflection.  Is there a standard function for this? Or is there a preferred method (regex?) for splitting the parameters correctly? It must handle '"' delimited strings that may contain spaces correctly, so I can't just split on ' '.  Example string:  string parameterString = @"/src:""C:\tmp\Some Folder\Sub Folder"" /users:""abcdefg@hijkl.com"" tasks:""SomeTask,Some Other Task"" -someParam foo";   Example result:  string[] parameterArray = new string[] {    @"/src:C:\tmp\Some Folder\Sub Folder",   @"/users:abcdefg@hijkl.com",   @"tasks:SomeTask,Some Other Task",   @"-someParam",   @"foo" };   I do not need a command-line parsing library, just a way to get the String[] that should be generated.  Update: I had to change the expected result to match what is actually generated by C# (removed the extra "'s in the split strings) The definitive guide to ConTeXt MkIV documentation Lagrange's theorem I don't understand left coset and Lagrange's theorem... I'm working on some project so please write me anything what could help me understand it better Block network access of a process? Can "Thanks for your edit!" banner be linkified with the Suggested Edit Link? Allow deleting a tag wiki or excerpt Sometimes a tag wiki excerpt or body ends up with unacceptable or useless content: plagiarized text that must be removed, or a totally unhelpful dictionary definition. (For example:  — and I've seen this situation many times before.)  The only way to get rid of that content is to submit replacement text that meets the minimum length requirement. This is not always easy as writing a decent wiki, and especially a decent excerpt, requires subject knowledge.  Currently the users or even moderators who are alerted to unacceptable content in a tag wiki cannot remove that content without providing their own, which they are not always in a position to do. Yet these wikis would be better off with no content than with either unacceptable or unhelpful content, or some content written by a non-expert in a hurry.  Please provide a way for users to blank a tag wiki excerpt or body. I'm not sure what the reputation requirement should be: same mechanism as for tag wiki edits (suggested edits with approval), or only done directly by a user with the trusted user (20k) privilege, or moderator-only. A little look through an etymology dictionary shows that the root is Latin gigas with adjective form gigant.  So in its derivation to English, why did the second "g" get retained in gigantic but was dropped from giant?  I have an inkling that the word giant may have travelled through French on its way to English, where it may have been pronounced "gee-yant" or "jee-yant" with a change to the second "g" that was then dropped when taken into English.  However, the "g" is retained as a hard "g" in gigantic. I want to convert .mov to .mp4! I saved the video from iMovie but it is in .mov format! How do I convert it to .mp4?  I'm using a MacBook and I want to share it to my phone, but my phone can't open .mov format video. When electric dipole placed in non uniform electric field, what is the approach to calculate torque acting on it? Can it be zero? How to link data to a polygon ArcMap 10.3 I have a map with different polygons (118). Each of this polygons represent diferent vegetation types.  For each of those polygons I have data of which species there is and how abundant they are (the abundance is measured with a scale from 1 to 3).  I would like to "link" (I am sorry if its not the correct way of name it) the data of which species and abundance there is in each of those polygons.   I would like afterwards to be able of selecting the different polygons containing the same abundance and species.  In the polygons I created there is no atributes associated other than (FID, shape and Id. the 3 of them created alone by the program when I drew them) and the tables I have in excel with the data I want to "link" to the polygons contain a column called species and another abundance.  As you can see, I'm pretty new using the program...    As I have tried to do what you all suggest in the comments down here, and I couldn't achieve what I was wanting to do (provably because of my bad explanation before...)  I leave a picture:  As you can see in the attribute table, that is how every attribute table of each polygon (which represents one area) looks like. On the right there is how I have my data in excel. Could you please suggest something I could do in order to add to the polygons attribute table the data belonging of species and its abundances (polygon number 1 has to have all the species (Acer mons, Acer pseu, Acer repens….) and its abundance (which are the numbers of the row Area1). the weak form of 'on' I am confused at whether or not there is a weak form at preposition's 'ON'. I've checked at some dictionaries at Cambridge and Oxford dictionary, they don't mention on the weak form's pronunciation. However, I, am a Japanese, checked at English-Japanese dictionaries, they mention on the weak form as /ən/.  For example, is there the difference of pronunciation between 'It goes on' and 'There is an apple on the table' in connected speech?  Does it exist?  Thanks Yuichi  *It's Edited iMessage doesn't say "delivered" or "not delivered" I sent an iMessage from my iPod touch to my friends iphone on Monday. It didn't say delivered or not delivered. It was just nothing. His phone is on (I know because my other friends are iMessaging him) and my friend said her messages don't say "delivered" at the bottom but they still talk. Mine always say delivered at the bottom. So is this an error, like it didn't go through, or is he just ignoring me? sort but keep header line at the top I am getting output from a program that first produces one line that is a bunch of column headers, and then a bunch of lines of data. I want to cut various columns of this output and view it sorted according to various columns. Without the headers, the cutting and sorting is easily accomplished via the -k option to sort along with cut or awk to view a subset of the columns. However, this method of sorting mixes the column headers in with the rest of the lines of output. Is there an easy way to keep the headers at the top? Without recasting and in lieu of unsightly suspensive hyphenation, could these work? The en dash (which means "to") is used between the figures, and the hyphens are used in the compound modifier. To me, the examples below are concise and clear.  Do you agree that the examples below are 100% punctuated correctly--yes or no?  45–50-year-old men  10–20-mile radius  $45–$55-million-per-year industry  $100,000–$150,000-a-year savings  10–15-degree temperature difference  $2–$5-per-day service fees  45–75-cent-a-week raises  55–65-mph speed zone  15–20-ounce steaks  20%–40%-a-year tax increases What does The Doctor's Speech in The Rings of Akhaten refer to? I recently watched the brilliant speech from The Rings of Akhaten again. For those who haven't seen it or don't remember it:     I walked away from the last Great Time War. I marked the passing of   the Time Lords. I saw the birth of the universe and I watched as time   ran out, moment by moment, until nothing remained. No time. No space.   Just me. I walked in universes where the laws of physics were devised   by the mind of a mad man. I've watched universes freeze and creations   burn. I've seen things you wouldn't believe. I have lost things you   will never understand. And I know things. Secrets that must never be   told. Knowledge that must never be spoken. Knowledge that will make   parasite gods blaze. So come on, then. Take it! Take it all, baby!   Have it! You have it all!   Some of these I understand:     I walked away from the last Great Time War.    Clear enough     I marked the passing of the Time Lords.   Again makes sense, given he "killed" them.     I saw the birth of the universe and I watched as time ran out, moment by moment, until nothing remained. No time. No space. Just me. I walked in universes where the laws of physics were devised by the mind of a mad man. I've watched universes freeze and creations burn.   I'm very vague on this put is some of it related to The Big Bang?     I've seen things you wouldn't believe. I have lost things you will never understand. And I know things. Secrets that must never be told. Knowledge that must never be spoken. Knowledge that will make parasite gods blaze.   Possibly relating to the question which must never be answered, but at this point we've not been to Trenzalore so does he even know what knowledge is and why?  What do the unknown sections of these speech refer to? How to efficiently find positions of duplicates? I write financial applications where I constantly battle the decision to use a double vs using a decimal.  All of my math works on numbers with no more than 5 decimal places and are not larger than ~100,000. I have a feeling that all of these can be represented as doubles anyways without rounding error, but have never been sure.  I would go ahead and make the switch from decimals to doubles for the obvious speed advantage, except that at the end of the day, I still use the ToString method to transmit prices to exchanges, and need to make sure it always outputs the number I expect. (89.99 instead of 89.99000000001)  Questions:   Is the speed advantage really as large as naive tests suggest? (~100 times) Is there a way to guarantee the output from ToString to be what I want? Is this assured by the fact that my number is always representable?   UPDATE: I have to process ~ 10 billion price updates before my app can run, and I have implemented with decimal right now for the obvious protective reasons, but it takes ~3 hours just to turn on, doubles would dramatically reduce my turn on time. Is there a safe way to do it with doubles?