All code for this episode can be found on the following GitHub page. GitHub Repo Directory: https://github.com/nkphysics/Computational-Linear-Algebra-/tree/master/7_Cholesky In this 7th video in this computational linear algebra series we cover a higher level variant of the LU Decomposition called the Choleksy Decomposition. The Choleksy decomposition's key benefit is that there we will only need to keep track of one lower triangular matrix, generally referred to as the Cholesky Factor. If we need to get back to our original matrix we can just multiply our lower triangular matrix (Cholesky Factor) by its transpose. By keeping track on only one matrix (the Choleksy Factor) we greatly improve out performance computationally. The one key initial condition which allows us to do a Cholesky decomposition though is that our matrix we want to decompose must be considered "positive definite." For more information on positive definiteness please see the following online resources: MIT Mini Lecture #1 : https://youtu.be/ojUQk_GNQbQ MIT Lecture: https://youtu.be/xsP-S7yKaRA MIT Mini Lecture #2: https://youtu.be/lpnY5QVjU5w Quick Tutorial on checking positive definiteness: https://youtu.be/ttMZB5Gm_fM

All credit goes to Griffiths for writing a fantastic quantum mechanics textbook. In this video we work through part A of problem 1.5 out of Griffiths Quantum mechanics.

This is just a quick discussion I wanted to have with all of my viewers were I answer some of your questions and comments. I mainly answer the questions "How did you learn NICER data processing?" I still cannot find the link to the NICER help desk email. If/when I find that email I will post is in a pinned comment. Find the recorded NICER Workshop videos here: https://heasarc.gsfc.nasa.gov/docs/nicer/data_analysis/workshops/index.html#spring21 I decided at the last minute not to include my twitter page so I am not mixing streams. Here is my github: https://github.com/nkphysics

AutoNICER is a bit of software I developed to automate the procedure of retrieving and reducing data gathered with the NICER mission. This video highlights the functionality of autoNICER and how to use it. autoNICER on GitHub: https://github.com/nkphysics/autoNICER autoNICER on PyPI: https://pypi.org/project/autonicer/ Contents: 00:00 - Intro 02:30 - Evidence 04:33 - GitHub Repository 04:45 - Prerequisites 05:50 - Installation 06:34 - HEASarc Archive 07:00 - Running autoNICER 09:24 - Selecting Datasets 13:45 - Retrieving and Reducing Data 15:57 - Details on Data Reduction commands 17:26 - Summary of run 18:24 - Output Log 19:55 - Contributing 21:23 - Future Plans 23:45 - Where I need help 26:04 - Conclusion DISCLAIMER: I (the creator of this video) am not affiliated with NASA, any space flight center, any NASA mission or any university or research institute. I am an independent researcher who utilizes HEASoft and the NICER mission's archival data to facilitate my own independent research into neutron stars. Visit NICER at HEASARC: https://heasarc.gsfc.nasa.gov/docs/nicer/ Check out HEASoft: https://heasarc.gsfc.nasa.gov/docs/nicer/