Proof of subordinate matrix norm equality

Proof of subordinate matrix norm equality

Let cdot_v be a norm in mathbbKn and Q in M_nmathbbK a regular matrix. We define cdot_v: mathbbKn rightarrow mathbbR such that X_vQX_v. Prove that cdot_v is also a norm. Let cdot_M and cdot_M their respective subordinate matrix norms in M_nmathbbK. Prove that forall A in M_nmathbbKn it is true that A_MQAQ-1_M. My definition of subordinate matrix norm is the following: If cdot_v is a norm then its subordinate matrix norm is A_M max_Xneq0 fracAX_vX_vmax_X1 AX_vmax_Xleq1 AX_v. The first question is pretty straight forward but Im stuck in the second one. First of all, we notice that: A_M max_Xneq0 fracAX_vX_v max_Xneq0 fracQAX_vQX_v. QAQ-1_M max_Xneq0 fracQAQ-1X_vX_v. I ve tried to prove that A_M leq QAQ-1_M and A_M geq QAQ-1_M playing with this inequality that has been useful other times when proving norm inequalities: AX_v leq A_M X_v forall A in M_nmathbbK, forall X in mathbbKn. But I have failed to prove any of both inequalities.

Комментарии

Отправить комментарий

Популярные сообщения из этого блога

Skipping acquire of configured file 'contrib/binary-i386/Packages' as repository … doesn't support architecture 'i386'

Skipping acquire of configured file 'contrib/binary-i386/Packages' as repository … doesn't support architecture 'i386' I installed Ubuntu 18.04 and then while installing Virtualbox i get the i386 error message after I did: sudo apt-get update Get:1 http:nl.archive.ubuntu.comubuntu bionic InRelease 242 kB Hit:2 http:security.ubuntu.comubuntu bionic-security InRelease Hit:3 http:ppa.launchpad.netdanielrichter2007grub-customizerubuntu bionic InRelease Hit:4 http:nl.archive.ubuntu.comubuntu bionic-updates InRelease Hit:5 http:nl.archive.ubuntu.comubuntu bionic-backports InRelease Get:6 http:download.virtualbox.orgvirtualboxdebian bionic InRelease 4429 B Get:7 http:download.virtualbox.orgvirtualboxdebian bioniccontrib amd64 Packages 1426 B Fetched 248 kB in 1s 209 kBs Reading package lists... Done N: Skipping acquire of configured file contribbinary-i386Packages as repository http:download.virtualbox.orgvirtualboxdebian bionic InRelease doesnt support architecture i386 ...
Далее...

Connection string for MariaDB using ODBC

Connection string for MariaDB using ODBC What is the connection string for using MariaDB with ODBC Im guessing its something like DRIVERMariaDB ODBC 5.1 Driver; SERVERLOCALHOST; PORT3306; DATABASEDatabaseName; UIDroot; PASSWORDpassword;OPTION3; Connection strings seems to show strings for MySQL but not MariaDB. MariaDB seems to have a lot of connection strings for Access, SQL Lite, excel, etc ... What have I missed Although this is late answer, but MariaDB have that documented here SQLWCHAR ConnStr LDriverMariaDB ODBC 2.0 Driver;Serverlocalhost;UIDodbc_user;PWDodbc_pw;DBodbc_test;Port3306;
Далее...

Celery like system based on django channels

Celery like system based on django channels According to the docs of django channels: http:channels.readthedocs.ioenlatestconcepts.htmlhighlightcelerynext-steps One thing channels do not do, however, is guarantee delivery. If you need certainty that tasks will complete, use a system designed for this with retries and persistence e.g. Celery, or alternatively make a management command that checks for completion and re-submits a message to the channel if nothing is completed rolling your own retry logic, essentially. I worked with celery some years ago. Yes, it is great, it is big, it is too much. I would like to avoid it. I am searching a simple tasks queue with guarantee delivery and a re-submission on failure. An other alternative would be python-rq. But this has other disadvantages like using pickle data format instead of json. A friend gave me an advice: https:github.comfurious-lukedjango-cq Looks good. From the docs An attempt to implement a distributed task queue ...
Далее...