matrices – Determine unknown matrix function of particular form from known points

I encountered the following problem recently in a practical context.

Fix $n ge 1$.
Suppose $f$ is an unknown function $mathbb C ^ {n times n} to mathbb C ^ {n times n}$ of the form
$$ X mapsto B^{-1} (X – A) (D B^{-1} (X – A) + C)^{-1} $$
for some $A, B, C, D in mathbb C ^ {n times n}$ with $B,C$ invertible.

  1. What is the minimum number of pairs $(X_i, f(X_i))$ needed to determine $f$?
  2. Given such a list of pairs $(X_1, f(X_1)), dots, (X_k, f(X_k))$ and an $X$, how does one compute $f(X)$?

I fear this problem may be too simple for MathOverflow;
however, it lies outside my area of expertise and I will accept a reference to somewhere dealing with this sort of problem.
Thank you.

hash – Bijective function with unknown reciprocal function

I have a use case where I need to build a unique identifier for my users with the email address and the “family member number”. However, the two personal informations used to build the identifier must be hidden. I thought using a hash function for that but there is a risk of collision.

Should I still use a hashing function for that, or should I use some kind of bijective function with unknown reciprocal, if such kind of function exists?

[Vn5socks.net] Auto update 24/7 – Good socks 9h45 PM


LIVE ~ 5.63.10.198:58418 | 0.274 | Unknown | Unknown | Unknown | Iran, Islamic Republic of | Checked at vn5socks.net
LIVE ~ 64.225.64.126:40001 | 0.283 | Atlanta | GA | 30303 | United States | Checked at vn5socks.net
LIVE ~ 79.124.62.26:443 | 0.209 | Svoge | 58 | Unknown | Bulgaria | Checked at vn5socks.net
LIVE ~ 41.78.24.126:9999 | 0.501 | Unknown | Unknown | Unknown | Kenya | Checked at vn5socks.net
LIVE ~ 104.238.111.218:40215 | 0.42 | Unknown | Unknown | Unknown | Unknown | Checked at vn5socks.net
LIVE ~ 108.61.75.207:9000 | 0.244 | Piscataway | NJ | 08854 | United States | Checked at vn5socks.net
LIVE ~ 134.209.100.103:32534 | 0.035 | Pleasanton | CA | 94588 | United States | Checked at vn5socks.net
LIVE ~ 157.245.231.94:9090 | 0.189 | Eugene | OR | 97402 | United States | Checked at vn5socks.net
LIVE ~ 158.69.243.148:9999 | 0.256 | Lake Forest | CA | 92630 | United States | Checked at vn5socks.net
LIVE ~ 218.87.174.26:55443 | 0.189 | Beijing | 22 | Unknown | China | Checked at vn5socks.net
LIVE ~ 159.89.237.201:40001 | 0.267 | Vancouver | BC | v7y1j7 | Canada | Checked at vn5socks.net
LIVE ~ 170.106.151.211:1089 | 0.195 | Parsippany | NJ | 07054 | United States | Checked at vn5socks.net
LIVE ~ 206.189.158.28:37884 | 0.053 | San Mateo | CA | 94404 | United States | Checked at vn5socks.net
LIVE ~ 185.14.31.113:443 | 0.28 | Unknown | Unknown | Unknown | Europe | Checked at vn5socks.net
LIVE ~ 188.120.245.247:55432 | 0.292 | Moscow | 48 | Unknown | Russian Federation | Checked at vn5socks.net
LIVE ~ 220.248.188.75:17211 | 0.429 | Unknown | Unknown | Unknown | China | Checked at vn5socks.net


FireHeaven
Reviewed by FireHeaven on
.
[Vn5socks.net] Auto update 24/7 – Good socks 9h45 PM
LIVE ~ 5.63.10.198:58418 | 0.274 | Unknown | Unknown | Unknown | Iran, Islamic Republic of | Checked at vn5socks.net
LIVE ~ 64.225.64.126:40001 | 0.283 | Atlanta | GA | 30303 | United States | Checked at vn5socks.net
LIVE ~ 79.124.62.26:443 | 0.209 | Svoge | 58 | Unknown | Bulgaria | Checked at vn5socks.net
LIVE ~ 41.78.24.126:9999 | 0.501 | Unknown | Unknown | Unknown | Kenya | Checked at vn5socks.net
LIVE ~ 104.238.111.218:40215 | 0.42 | Unknown | Unknown |

Rating: 5



.

ruby – “unknown encoding name” when using gem command

On Windows 10 using the Cygwin environment, I get the following error:

 $ gem list
 ERROR:  Loading command: list (ArgumentError)
      unknown encoding name - CP20127
 ERROR:  While executing gem ... (NoMethodError)
      undefined method `invoke_with_build_args' for nil:NilClass

I have

 $ gem --version
 3.0.    
 $ ruby --version
 ruby 2.6.4p104 (2019-08-28 revision 67798) (x86_64-cygwin)
 $ echo $LANG
 en_GB

running in a mintty terminal (version 3.1.6)

I haven’t used the gem command for months. It did work once, but of course any of the components involved, have been updated in between several times. I don’t know where the encoding CP20127 comes from. It does not look like a valid encoding name or Windows code page name to me, but it indeed seems to be Windows is using:

$ chcp
Aktive Codepage: 20127

I never fiddled around with the code page and I wonder where this setting could come from, and why it could affect my gem command.

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LIVE ~ 157.245.231.94:9090 | 0.193 | Eugene | OR | 97402 | United States | Checked at vn5socks.net
LIVE ~ 159.89.237.201:40001 | 0.239 | Vancouver | BC | v7y1j7 | Canada | Checked at vn5socks.net
LIVE ~ 167.71.172.18:9060 | 0.26 | New York | NY | 10020 | United States | Checked at vn5socks.net
LIVE ~ 47.49.12.165:36959 | 0.262 | Ottawa | ON | k1y4h7 | Canada | Checked at vn5socks.net
LIVE ~ 64.225.64.126:40001 | 0.293 | Atlanta | GA | 30303 | United States | Checked at vn5socks.net
LIVE ~ 188.120.245.247:55432 | 0.293 | Moscow | 48 | Unknown | Russian Federation | Checked at vn5socks.net
LIVE ~ 185.14.31.113:443 | 0.28 | Unknown | Unknown | Unknown | Europe | Checked at vn5socks.net
LIVE ~ 170.106.151.211:1089 | 0.243 | Parsippany | NJ | 07054 | United States | Checked at vn5socks.net
LIVE ~ 39.109.115.242:999 | 0.045 | Unknown | Unknown | Unknown | Hong Kong | Checked at vn5socks.net
LIVE ~ 108.61.75.207:9000 | 0.241 | Piscataway | NJ | 08854 | United States | Checked at vn5socks.net
LIVE ~ 80.251.208.230:3160 | 0.209 | Unknown | Unknown | Unknown | Russian Federation | Checked at vn5socks.net
LIVE ~ 80.251.208.230:2054 | 0.207 | Unknown | Unknown | Unknown | Russian Federation | Checked at vn5socks.net
LIVE ~ 41.78.24.126:9999 | 0.561 | Unknown | Unknown | Unknown | Kenya | Checked at vn5socks.net
LIVE ~ 220.248.188.75:17211 | 0.529 | Unknown | Unknown | Unknown | China | Checked at vn5socks.net
LIVE ~ 178.162.202.44:1753 | 0.25 | Unknown | Unknown | Unknown | Germany | Checked at vn5socks.net


FireHeaven
Reviewed by FireHeaven on
.
[Vn5socks.net] Auto update 24/7 – Good socks 10h30 PM
LIVE ~ 158.69.243.148:9999 | 0.241 | Lake Forest | CA | 92630 | United States | Checked at vn5socks.net
LIVE ~ 82.165.137.115:7061 | 0.284 | Unknown | Unknown | Unknown | Germany | Checked at vn5socks.net
LIVE ~ 157.245.231.94:9090 | 0.193 | Eugene | OR | 97402 | United States | Checked at vn5socks.net
LIVE ~ 159.89.237.201:40001 | 0.239 | Vancouver | BC | v7y1j7 | Canada | Checked at vn5socks.net
LIVE ~ 167.71.172.18:9060 | 0.26 | New York | NY | 10020 |

Rating: 5



.

Postfix sending an email to unknown user every minute

I get this loop in my /var/log/maillog every minute. I don’t know what is the source, and who is sending this. I don’t have user apache in my server. I have been trying to fix my postfix problems, and this problem has my attention. I hope someone can help me fix this, or at least guide me to how to fix it.

Thank you 🙂

Oct 26 18:25:01 mail postfix/lmtp(4429): 53EC219E08F3: to=<apache@xxxxxx.org>, relay=mail.xxxxxx.org(private/dovecot-lmtp), delay=0.11, delays=0.06/0/0/0.05, dsn=5.1.1, status=bounced (host mail.xxxxxx.org(private/dovecot-lmtp) said: 550 5.1.1 <apache@xxxxxx.org> User doesn't exist: apache@xxxxxx.org (in reply to RCPT TO command))

Oct 26 18:25:01 mail dovecot: lmtp(4276): Disconnect from local: Successful quit
Oct 26 18:25:01 mail postfix/qmgr(2235): 53EC219E08F3: removed

[Vn5socks.net] Auto update 24/7 – Good socks 5h00 PM


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LIVE ~ 185.14.31.113:443 | 0.293 | Unknown | Unknown | Unknown | Europe | Checked at vn5socks.net
LIVE ~ 80.251.208.230:2054 | 0.17 | Unknown | Unknown | Unknown | Russian Federation | Checked at vn5socks.net
LIVE ~ 108.61.75.207:9000 | 0.241 | Piscataway | NJ | 08854 | United States | Checked at vn5socks.net
LIVE ~ 64.225.64.126:40001 | 0.289 | Atlanta | GA | 30303 | United States | Checked at vn5socks.net
LIVE ~ 167.71.172.18:9060 | 0.271 | New York | NY | 10020 | United States | Checked at vn5socks.net
LIVE ~ 157.245.231.94:9090 | 0.189 | Eugene | OR | 97402 | United States | Checked at vn5socks.net
LIVE ~ 39.109.115.242:999 | 0.035 | Unknown | Unknown | Unknown | Hong Kong | Checked at vn5socks.net
LIVE ~ 220.248.188.75:17211 | 0.352 | Unknown | Unknown | Unknown | China | Checked at vn5socks.net
LIVE ~ 82.165.137.115:7061 | 0.276 | Unknown | Unknown | Unknown | Germany | Checked at vn5socks.net
LIVE ~ 18.177.13.247:443 | 0.133 | Cambridge | MA | 02139 | United States | Checked at vn5socks.net
LIVE ~ 41.78.24.126:9999 | 0.495 | Unknown | Unknown | Unknown | Kenya | Checked at vn5socks.net
LIVE ~ 51.79.69.153:1337 | 0.26 | Unknown | Unknown | Unknown | United Kingdom | Checked at vn5socks.net
LIVE ~ 170.106.151.211:1089 | 0.203 | Parsippany | NJ | 07054 | United States | Checked at vn5socks.net
LIVE ~ 188.120.245.247:55432 | 0.267 | Moscow | 48 | Unknown | Russian Federation | Checked at vn5socks.net


FireHeaven
Reviewed by FireHeaven on
.
[Vn5socks.net] Auto update 24/7 – Good socks 5h00 PM
LIVE ~ 159.89.237.201:40001 | 0.249 | Vancouver | BC | v7y1j7 | Canada | Checked at vn5socks.net
LIVE ~ 60.170.111.51:30022 | 0.29 | Hefei | 01 | Unknown | China | Checked at vn5socks.net
LIVE ~ 80.251.208.230:3160 | 0.187 | Unknown | Unknown | Unknown | Russian Federation | Checked at vn5socks.net
LIVE ~ 185.14.31.113:443 | 0.293 | Unknown | Unknown | Unknown | Europe | Checked at vn5socks.net
LIVE ~ 80.251.208.230:2054 | 0.17 | Unknown | Unknown | Unknown |

Rating: 5



.

[Vn5socks.net] Auto update 24/7 – Good socks 12h30 PM


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LIVE ~ 80.251.208.230:2054 | 0.285 | Unknown | Unknown | Unknown | Russian Federation | Checked at vn5socks.net
LIVE ~ 158.69.243.148:9999 | 0.35 | Lake Forest | CA | 92630 | United States | Checked at vn5socks.net
LIVE ~ 159.89.237.201:40001 | 0.386 | Vancouver | BC | v7y1j7 | Canada | Checked at vn5socks.net
LIVE ~ 79.124.62.26:443 | 0.212 | Svoge | 58 | Unknown | Bulgaria | Checked at vn5socks.net
LIVE ~ 64.225.64.126:40001 | 0.423 | Atlanta | GA | 30303 | United States | Checked at vn5socks.net
LIVE ~ 185.14.31.113:443 | 0.293 | Unknown | Unknown | Unknown | Europe | Checked at vn5socks.net
LIVE ~ 170.106.151.211:1089 | 0.244 | Parsippany | NJ | 07054 | United States | Checked at vn5socks.net
LIVE ~ 167.71.172.18:9060 | 0.36 | New York | NY | 10020 | United States | Checked at vn5socks.net
LIVE ~ 157.245.231.94:9090 | 0.212 | Eugene | OR | 97402 | United States | Checked at vn5socks.net
LIVE ~ 39.109.115.242:999 | 0.024 | Unknown | Unknown | Unknown | Hong Kong | Checked at vn5socks.net
LIVE ~ 220.248.188.75:17211 | 0.391 | Unknown | Unknown | Unknown | China | Checked at vn5socks.net
LIVE ~ 18.177.13.247:443 | 0.14 | Cambridge | MA | 02139 | United States | Checked at vn5socks.net
LIVE ~ 188.120.245.247:55432 | 0.262 | Moscow | 48 | Unknown | Russian Federation | Checked at vn5socks.net
LIVE ~ 47.49.12.169:15615 | 0.355 | Ottawa | ON | k1y4h7 | Canada | Checked at vn5socks.net
LIVE ~ 51.79.69.153:1337 | 0.31 | Unknown | Unknown | Unknown | United Kingdom | Checked at vn5socks.net
LIVE ~ 178.162.202.44:1753 | 0.36 | Unknown | Unknown | Unknown | Germany | Checked at vn5socks.net


FireHeaven
Reviewed by FireHeaven on
.
[Vn5socks.net] Auto update 24/7 – Good socks 12h30 PM
LIVE ~ 80.251.208.230:3160 | 0.271 | Unknown | Unknown | Unknown | Russian Federation | Checked at vn5socks.net
LIVE ~ 108.61.75.207:9000 | 0.245 | Piscataway | NJ | 08854 | United States | Checked at vn5socks.net
LIVE ~ 80.251.208.230:2054 | 0.285 | Unknown | Unknown | Unknown | Russian Federation | Checked at vn5socks.net
LIVE ~ 158.69.243.148:9999 | 0.35 | Lake Forest | CA | 92630 | United States | Checked at vn5socks.net
LIVE ~ 159.89.237.201:40001 | 0.386 |

Rating: 5



.

[Vn5socks.net] Auto update 24/7 – Good socks 9h20 AM


LIVE ~ 158.69.243.148:9999 | 0.251 | Lake Forest | CA | 92630 | United States | Checked at vn5socks.net
LIVE ~ 159.89.237.201:40001 | 0.249 | Vancouver | BC | v7y1j7 | Canada | Checked at vn5socks.net
LIVE ~ 60.170.111.51:30022 | 0.29 | Hefei | 01 | Unknown | China | Checked at vn5socks.net
LIVE ~ 80.251.208.230:3160 | 0.187 | Unknown | Unknown | Unknown | Russian Federation | Checked at vn5socks.net
LIVE ~ 185.14.31.113:443 | 0.293 | Unknown | Unknown | Unknown | Europe | Checked at vn5socks.net
LIVE ~ 80.251.208.230:2054 | 0.17 | Unknown | Unknown | Unknown | Russian Federation | Checked at vn5socks.net
LIVE ~ 108.61.75.207:9000 | 0.241 | Piscataway | NJ | 08854 | United States | Checked at vn5socks.net
LIVE ~ 64.225.64.126:40001 | 0.289 | Atlanta | GA | 30303 | United States | Checked at vn5socks.net
LIVE ~ 167.71.172.18:9060 | 0.271 | New York | NY | 10020 | United States | Checked at vn5socks.net
LIVE ~ 157.245.231.94:9090 | 0.189 | Eugene | OR | 97402 | United States | Checked at vn5socks.net
LIVE ~ 39.109.115.242:999 | 0.035 | Unknown | Unknown | Unknown | Hong Kong | Checked at vn5socks.net
LIVE ~ 220.248.188.75:17211 | 0.352 | Unknown | Unknown | Unknown | China | Checked at vn5socks.net
LIVE ~ 82.165.137.115:7061 | 0.276 | Unknown | Unknown | Unknown | Germany | Checked at vn5socks.net
LIVE ~ 18.177.13.247:443 | 0.133 | Cambridge | MA | 02139 | United States | Checked at vn5socks.net
LIVE ~ 41.78.24.126:9999 | 0.495 | Unknown | Unknown | Unknown | Kenya | Checked at vn5socks.net
LIVE ~ 51.79.69.153:1337 | 0.26 | Unknown | Unknown | Unknown | United Kingdom | Checked at vn5socks.net
LIVE ~ 170.106.151.211:1089 | 0.203 | Parsippany | NJ | 07054 | United States | Checked at vn5socks.net
LIVE ~ 188.120.245.247:55432 | 0.267 | Moscow | 48 | Unknown | Russian Federation | Checked at vn5socks.net


FireHeaven
Reviewed by FireHeaven on
.
[Vn5socks.net] Auto update 24/7 – Good socks 9h20 AM
LIVE ~ 158.69.243.148:9999 | 0.251 | Lake Forest | CA | 92630 | United States | Checked at vn5socks.net
LIVE ~ 159.89.237.201:40001 | 0.249 | Vancouver | BC | v7y1j7 | Canada | Checked at vn5socks.net
LIVE ~ 60.170.111.51:30022 | 0.29 | Hefei | 01 | Unknown | China | Checked at vn5socks.net
LIVE ~ 80.251.208.230:3160 | 0.187 | Unknown | Unknown | Unknown | Russian Federation | Checked at vn5socks.net
LIVE ~ 185.14.31.113:443 | 0.293 | Unknown | Unknown | Unknown

Rating: 5



.

[Vn5socks.net] Auto update 24/7 – Good socks 9h30 PM


LIVE ~ 158.69.243.148:9999 | 0.241 | Lake Forest | CA | 92630 | United States | Checked at vn5socks.net
LIVE ~ 60.170.111.51:30022 | 0.31 | Hefei | 01 | Unknown | China | Checked at vn5socks.net
LIVE ~ 159.89.237.201:40001 | 0.287 | Vancouver | BC | v7y1j7 | Canada | Checked at vn5socks.net
LIVE ~ 79.124.62.26:443 | 0.359 | Svoge | 58 | Unknown | Bulgaria | Checked at vn5socks.net
LIVE ~ 185.14.31.113:443 | 0.313 | Unknown | Unknown | Unknown | Europe | Checked at vn5socks.net
LIVE ~ 64.225.64.126:40001 | 0.291 | Atlanta | GA | 30303 | United States | Checked at vn5socks.net
LIVE ~ 167.71.172.18:9060 | 0.248 | New York | NY | 10020 | United States | Checked at vn5socks.net
LIVE ~ 157.245.231.94:9090 | 0.186 | Eugene | OR | 97402 | United States | Checked at vn5socks.net
LIVE ~ 125.123.122.26:39823 | 0.289 | Jiaxing | 02 | Unknown | China | Checked at vn5socks.net
LIVE ~ 82.165.137.115:7061 | 0.329 | Unknown | Unknown | Unknown | Germany | Checked at vn5socks.net
LIVE ~ 39.109.115.242:999 | 0.022 | Unknown | Unknown | Unknown | Hong Kong | Checked at vn5socks.net
LIVE ~ 47.49.12.165:36959 | 0.296 | Ottawa | ON | k1y4h7 | Canada | Checked at vn5socks.net
LIVE ~ 18.177.13.247:443 | 0.249 | Cambridge | MA | 02139 | United States | Checked at vn5socks.net
LIVE ~ 51.79.69.153:1337 | 0.256 | Unknown | Unknown | Unknown | United Kingdom | Checked at vn5socks.net
LIVE ~ 170.106.151.211:1089 | 0.193 | Parsippany | NJ | 07054 | United States | Checked at vn5socks.net
LIVE ~ 188.120.245.247:55432 | 0.288 | Moscow | 48 | Unknown | Russian Federation | Checked at vn5socks.net
LIVE ~ 41.78.24.126:9999 | 0.554 | Unknown | Unknown | Unknown | Kenya | Checked at vn5socks.net


FireHeaven
Reviewed by FireHeaven on
.
[Vn5socks.net] Auto update 24/7 – Good socks 9h30 PM
LIVE ~ 158.69.243.148:9999 | 0.241 | Lake Forest | CA | 92630 | United States | Checked at vn5socks.net
LIVE ~ 60.170.111.51:30022 | 0.31 | Hefei | 01 | Unknown | China | Checked at vn5socks.net
LIVE ~ 159.89.237.201:40001 | 0.287 | Vancouver | BC | v7y1j7 | Canada | Checked at vn5socks.net
LIVE ~ 79.124.62.26:443 | 0.359 | Svoge | 58 | Unknown | Bulgaria | Checked at vn5socks.net
LIVE ~ 185.14.31.113:443 | 0.313 | Unknown | Unknown | Unknown | Europe | Checked

Rating: 5



.