Integral row reduction + Hermite normal form|Abstract Algebra Math Foundations 223 | NJ Wildberger

Описание: We have a careful look at getting a good basis of an integral linear space through a specific algorithm which is essentially that of Hermite normal form. Usually in linear algebra courses this is framed in terms of matrices, but here we are taking more of an mset point of view, but the idea is still very much the same. This algorithm is an integral version of Gaussian elimination or row reduction, familiar to undergraduates around the world.

Perhaps surprisingly, this integral version closely parallels Euclid's algorithm for finding the greatest common divisor of two (or possibly) more natural numbers. We will give an official definition of Hermite normal form for an mset of vexels.

On a different note, I am pleased to let you know about my UNSW colleague Daniel Chan's new YouTube channel, called Adventures in Mathematics. Daniel is a strong mathematician and a fine expositor, so I am sure you will find his lectures interesting and engaging! The link is
   / @danielchanmaths  


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Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary.

My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/...

My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things.

Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at https://www.openlearning.com/courses/... Please join us for an exciting new approach to one of mathematics' most important subjects!

If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at   / njwildberger   Your support would be much appreciated.

Here are the Insights into Mathematics Playlists:

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