Linear Algebra:Foundations to Frontiers -
Notes on Numerical Linear Algebra

An e-book that integrates the notes, answers to exercises, and a few (full lecture) videos created for an introductory graduate course on Numerical Linear Algebra taught by Robert van de Geijn at The University of Texas at Austin. The author is an expert and active researcher in the field who has published significant state-of-the-art papers on almost all subjects covered by the book. This material dovetails with the undergraduate text Linear Algebra: Foundations to Frontiers - Notes to LAFF With.

The undergraduate level Linear Algebra: Foundations to Frontiers materials were carefully designed to be an online course. It took a year of hard work on the part of several authors to design that course, create a book, and produce 250+ videos. In contrast, the graduate course is an ongoing project where Robert simply taped his lectures with a camera and made the same materials available to the world as he makes available to his own students. For some lectures, he forgot to turn on the camera... The real value is in his notes, LAFF - Notes on Numerical Linear Algebra, which has been an ongoing project for several years. Still, these are also a work in progress. In other words, these materials have not received the same level of tender loving care as their counter parts for LAFF - Notes to LAFF With.

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Who should LAFF some more?

Here are some people who may want to consider Linear Algebra: Foundations to Frontiers - Notes on Numerical Linear Algebra:

• The Veteran LAFFer. If you completed LAFF: Notes to LAFF With (or the related course offered by edX), then you are ready for this graduate level material.

• The Guide. What we also hope to deliver is a resource for someone who is an effective facilitator of learning (what some would call an instructor) to be used, for example, in a classroom setting. While this individual may or may not have our level of expertise in the domain of numerical linear algebra, what is important is that she/he can use these materials to guide, inspire, and teach.

  If you are teaching a graduate course on NLA, the following may be useful:

  • The order of the material follows for the most part the order in the book "Numerical Linear Algebra" by Trefethen and Bau. We like the fact that they start with orthogonality.
  • You may consider using our materials in addition to that book or as an alternative. Our experience is that mathematics students often prefer the book by Trefethen and Bau, and that engineering and/or computer science students relate positively to the way we present the various topics.

• The Refresher. At some point, a graduate student or practitioner of mathematics (in engineering, the physical sciences, the social sciences, business, and many other subjects) realizes that numerical linear algebra is fundamental to subjects in, for example, engineering, physical sciences, life sciences, statistics, computer science, and data sciences. This often happens after the individual has already completed a course on the subject and now he/she realizes it is time for a refresher. This material shines a different light on classical material and brings it up to date.

• The Graduate Student. If you need a background in numerical linear algebra and don't have time to take the course or you are taking the course and the book being used doesn't quite hit the spot, this may be the book for you. Importantly, whenever you run into a topic for which you feel you do not have the undergraduate background in linear algebra, you can refer back to LAFF - Notes to LAFF With.

If you are still trying to decide whether these materials are for you, you can simply download some of the materials and see!

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Ready to LAFF at the graduate level?

Please consider "pick your price" Publication of these materials is self-funded by the authors. We don't think videos of full length lectures is as effective as the kind of short videos incorporated in LAFF - Notes to LAFF With. You contributions may just convince us to improve the videos and create online activities. Pick your price! You determine what LAFF is worth to you. Thank you! If you reside OUTSIDE Texas (no sales tax!): Financially Strapped Student $20.00 USD Successful Professional $50.00 USD LAFF Lover $100.00 USD Other $35.00 USD If you reside in Texas (sales tax!): Financially Strapped Student $20.00 USD Successful Professional $50.00 USD LAFF Lover $100.00 USD Other $35.00 USD

For free Have a look before you purchase. Can't afford a contribution? Pay forward! Donate something small to a local charity, tutor someone in linear algebra, do something good for the world. It is a work in progress! It is ok to wait to pay until it becomes more refined. Already bought a copy and want a newer release? Help yourself! Some might think LAFF is priceless and that it would be wrong to put a price on it. Click to download materials.

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Need to LAFF Less?

The above introductory graduate materials assume an undergraduate background in linear algebra. If you find you are not quite ready, consider Linear Algebra: Foundations to Frontiers - Notes to LAFF With.