Is one-generator matrix subring linearly representable? If so, how hard it is?

Suppose $ A\in GL_n(\mathbb R)$ , i.e. a $ n\times n$ invertible matrix over a ring $ \mathbb R$ . My question is as follows:

(1) Is $ \mathbb R_A=\langle A,+,\cdot \rangle$ a subring of $ M_n(\mathbb R)$ , where $ +$ and $ \cdot$ mean matrix addition and multiplication, respectively.

(2) Does $ \mathbb R_A$ exist linear representation in the following sense: For each matrix $ B\in \mathbb R_A$ , there is $ a_1,\cdots, a_{\ell}\in\mathbb R$ such that $ B=a_1A+a_2A^2+\cdots+a_{\ell}A^{\ell}$ for some $ \ell\leq n^2$ ?

Can’t delete files from external hard drive / Input – Output error

I can’t delete some files from a external hard drive. This the result i get in the terminal when i try to do it:

camilo@camilo-S400CA:~$   sudo rm -r '/media/camilo/TOSHIBA EXT/Descargas' [sudo] password for camilo:  rm: cannot remove '/media/camilo/TOSHIBA EXT/Descargas/Dragon Ball Z Season 1 BrRip FullHD 1080p Spa Latino, Japanese, English + Sub/14. Princess Snake.mkv.part': No such file or directory rm: cannot remove '/media/camilo/TOSHIBA EXT/Descargas/Dragon Ball Z Season 1 BrRip FullHD 1080p Spa Latino, Japanese, English + Sub/38. Nursing Wounds.mkv.part': Input/output error rm: cannot remove '/media/camilo/TOSHIBA EXT/Descargas/Violeta Parra - 26 discos/Violeta Parra - 1997 - Paroles Musicales': Input/output error rm: cannot remove '/media/camilo/TOSHIBA EXT/Descargas/Violeta Parra - 26 discos/Violeta Parra - 1956 - Violeta Parra, acompañada de guitarra (Folklore de Chile Vol. II)/13 - Tonada del medio.mp3': Is a directory rm: cannot remove '/media/camilo/TOSHIBA EXT/Descargas/Violeta Parra - 26 discos/Violeta Parra - 1956 - Violeta Parra, canto y guitarra (Folklore de Chile Vol. I)/17 - La paloma ingrata.mp3': No such file or directory rm: cannot remove '/media/camilo/TOSHIBA EXT/Descargas/Violeta Parra - 26 discos/Violeta Parra - 1971 - Canciones Casa de las Americas': Input/output error rm: cannot remove '/media/camilo/TOSHIBA EXT/Descargas/Violeta Parra - 26 discos/Violeta Parra - 2003 - Memoria del cantar popular/05 - Que dirá el santo padre.mp3': No such file or directory rm: cannot remove '/media/camilo/TOSHIBA EXT/Descargas/Violeta Parra - 26 discos/Violeta Parra - 2004 - Grandes Exitos': No such file or directory rm: cannot remove '/media/camilo/TOSHIBA EXT/Descargas/Violeta Parra - 26 discos/Violeta Parra - 2004 - Puras Cuecas/23 - Aromas.mp3': No such file or directory camilo@camilo-S400CA:~$   sudo rm -r '/media/camilo/TOSHIBA EXT/Juegos/Doom' rm: cannot remove '/media/camilo/TOSHIBA EXT/Juegos/Doom/Mods/Doom 64/D64RTR_BRIGHTMAPS.PK3': Input/output error rm: cannot remove '/media/camilo/TOSHIBA EXT/Juegos/Doom/Mods/Doom 64/D64RTR_CHANGELOG.TXT': Input/output error rm: cannot remove '/media/camilo/TOSHIBA EXT/Juegos/Doom/Mods/Doom 64/D64RTR_INSTRUCTIONS.TXT': Input/output error rm: cannot remove '/media/camilo/TOSHIBA EXT/Juegos/Doom/Mods/Doom 64/D64RTR_README.TXT': Input/output error camilo@camilo-S400CA:~$    

Apart from these the drive is working ok.

I tried to run a SMART test to the drive but i was unable to because according to GSmartControl and GnomeDisks the hd does seem to have Smart Control, which is weird because i buyed this thing like two or three months ago.

Thanks in advance!

How to remove Ubuntu when I installed on wrong hard drive?

I feel this is a stupid question. So basically I have two drives one 120gb ssd and one 1tb hdd. I want to install systems and regular used programs on ssd and put data in HDD. However, i messed up by installing on hdd. How do I transfer the system to the ssd? Or how do I remove the installation on hdd? By the way, the version I installed is Ubuntu 18.04 LTS

Any tool available for free that could recover data from a hard disk in windows?

The question is pretty much self-explanatory. I’m trying to recover data in Windows 8.1 pro. I downloaded and installed Disk Drill. The software worked perfect but the issue is it only provides a maximum limit of 500 MB data to recover. Is there any tool which doesn’t have this restriction and by the help of which I could recover all of my data.

Hard problem about way arrgane [on hold]

The landlord of Numberland has a piece of land of size 500m x 500m. He divided the land into 25 land lots of size 100m x 100m to supply to 25 members of the Senate. Some members of the Senate are enemies, so they do not want to live in neighboring region.Know that every senator member has no more than 3 enemies. Prove that the landlord can divide plots for 25 members of the Senate so that the land of two members who are each other’s enemies does not have the common side.

Recover Deleted Data from Malfunctioning Hard Drive

I deleted some data accidentally on my Macbook a while ago, and then a couple weeks later the hard drive failed. Now my Macbook can’t start normally. I took it to an Apple store and they told me they could replace the hard drive but I need to go somewhere else to extract the data. Is it possible for me to recover the data I deleted? Thank you in advance!

Hard Sudoku Puzzle Creation Algorithm in quadratic time

To avoid backtracking, I’ve generated an algorithm with some research into a polynomial time algorithm.

Overall, I’m looking for constructive-criticism, improvement, recommendations, etc.

I’ve found out that if I control all parameters in the creation of a Sudoku puzzle I can generate the puzzle from a solution in quadratic time.

Here’s the summary of the entire description of the algorithm. Before you get into your reading.

Step 1 Follow the grid and puzzle generation method(mentioned at the end of the question).

Step 2 Enter for input l to generate a solution before generating the puzzle [8,5,9,6,1,2,4,3,7]

Step 3. Now generate the puzzle Example- Take the output of the complete grid and compare to the world’s hardest sudoku puzzle and arrange the elements in some algorthim(paper or computer) to match the below.

n = 0 l = input('Enter the first solved box to get a correct solution')  note when script asks for input you must write it like this  [1,2,3,4,5,6,7,8,9]  indices = [] for i in xrange(1, 1+len(l)):         indices.append(n % i)         n //= i         indices.reverse()          perm = l for index in indices:         perm.append(l.pop(index))         print(perm) 

2nd part of algorthim not yet implemented in the script

To convert the result(which is an horizantal solution) into human readable format follow this method.

You take the first three rows from the output

[1,2,3,4,5,6,7,8,9]  [1,2,3,4,5,6,7,8,9]  [1,2,3,4,5,6,7,8,9] 

and do this…. Line them up one by one side by side in this order and I’m seemingly always getting correct grids!!

Yeah, I know this isn’t in right order but just to show illustration

[1,2,3]

[4,5,6]

[7,8,9]

[1,2,3]

[4,5,6]

[7,8,9]

[1,2,3]

[4,5,6]

[7,8,9]

Here’s an actual output of a solution in horizontal format.

[9, 6, 1, 2, 4, 3, 7, 8, 5]  [6, 1, 2, 4, 3, 7, 8, 5, 9]  [1, 2, 4, 3, 7, 8, 5, 9, 6]  [2, 4, 3, 7, 8, 5, 9, 6, 1]  [4, 3, 7, 8, 5, 9, 6, 1, 2]  [3, 7, 8, 5, 9, 6, 1, 2, 4]  [7, 8, 5, 9, 6, 1, 2, 4, 3]  [8, 5, 9, 6, 1, 2, 4, 3, 7]  [5, 9, 6, 1, 2, 4, 3, 7, 8] 

Following the aforementioned method.

You get a correct Sudoku grid. (The checker says its correct every time I’ve ran it) I’ve taken out some elements to see if there’s a puzzle with 1 solution and behold.

[9 6 1][2 4 3][7 8 5]  [2 4 3][7 8 5][9 6 1]  [7 8 5][9 6 1][2 4 3]  [6 1 2][4 3 7][8 5 9]  [4 3 7][8 5 9][6 1 2]  [8 5 9][6 1 2][4 3 7]  [1 2 4][3 7 8][5 9 6]  [3 7 8][5 9 6][1 2 4]  [5 9 6][1 2 4][3 7 8] 

Pseudo-code

Python2.7

>>>World-s hardest Sudoku puzzle converted in vertical format  800000000003600000070090200050007000000045700000100030001000068008500010090000400   Manipulating your generated grid to match index by index of hardest puzzle. (This is making sure there should only be 1 solution)   961243785612437859124378596243785961437859612378596124785961243859612437596124378   Poof!! string manipulation done in linear time.  900000000002400000020070500040005000000059600000500020005000043009600030090000300 

(warning manual typos will happen if done by hand)

Converting into correct format with one solution only(supposedly)

— Solve this. Warning I’ve probably got typos.

900 040 050 000 005 000 000 000 430  002 000 096 400 000 000 000 059 300  020 005 900 070 000 003 500 200 000 

Since, I’ve made sure that the grids are always correct. I took a screenshot of Sudoku checker. Generating Complete Grids. Even the puzzles are seemingly always generated correctly in quadratic time.

enter image description here

Not enough testing has confirmed if every puzzle generated from this algorithm is correct, but every grid has been correct so far if you actually follow the method correctly.

http://www.birot.hu/sudoku.php

How to make a simple bitcoin hard fork

I am exploring bitcoin source code for some time and have successfully created a local bitcoin network with new genesis block.
Now i am trying to understand the process of hard forks (if i am using wrong terms here, i am referring to the one where the blockchain is split instead of mining a new genesis).
I am trying find this approach in BitcoinCash source code, but haven’t got anywhere so far except the checkpoints.

//UAHF fork block.   {478558, uint256S("0000000000000000011865af4122fe3b144e2cbeea86"           "142e8ff2fb4107352d43") } 

So for i understand that the above checkpoint is responsible for the chain split. But i am unable to find the location in source code where this rule is enforced, i.e. the code where it is specified to have a different block than bitcoin after block number 478558.
Can anyone set me into the right direction here?

Is it considered dual boot when I installed ubuntu in a separate hard drive?

I can’t seem to find an answer to my question so if someone knows a post that answers my question, I’d be grateful if you can send me there.

I have currently set up my laptop to have windows installed on a M.2 nvme and ubuntu on a separate internal HDD. When installing ubuntu, I took out the M.2 to make sure I didn’t wipe the wrong hard drive. Is this still considered dual booting since I have to go and change the boot order or is it still dual booting? Another question is will this configuration allow me to keep window’s fast start up and the bios’s fast startup or do I have to turn window’s fast start off? I tried booting up with secure boot on both drives and they work, albeit slowly. Thanks for the help!

I formated my hard drive with bitcoin core on it

First timer here

…I downloaded bitcoin core a few weeks ago until last week where it still had not synced so i started all over…I was originally waiting for BTC CORE to synchronize(I missed the part in the installation that stated I needed 220+ gb of free space)…I had to format BOOT ssd(256gb..also where I originally tried to save BTC CORE)…thats why it was taking so long and I purchased 1tb samsung evo. I’m wondering if my BTC address will be the same(since I never actually synced with the servers and since I am not using the same SSD where BTC CORE is being saved. However, it is the same SSD that windows is booting from but I had to reinstall windows.

I have now downloaded BTC CORE on my new SSD and it is synced. Unfortunately, I cant find my BTC and when I use a block explorer the funds are not there(I checked with a BE last week and the BTC was there… but pending or waiting to sync…now its not)

…did my BTC address change? will it ever sync with the older one so I can get my funds?

hope someone can help