Download LAFF - Linear Algebra: Foundations to Frontiers by Robert van de Geijn, Maggie Myers PDF

By Robert van de Geijn, Maggie Myers

LAFF all started as a tremendous Open on-line direction (MOOC) funded partially by means of the collage of Texas approach and the nationwide technological know-how beginning (grant ACI-1148125), created via Prof. Robert van de Geijn and Dr. Maggie Myers on the collage of Texas at Austin, and introduced at the edX platform . The fabrics stay on hand with edX via at the very least summer season 2014.

The "Notes to LAFF With" are a PDF booklet that turns into the "hub" by which the opposite LAFF fabric (e.g., the movies) might be accessed. It is going past the notes that have been published as a part of the edX MOOC via additionally supplying an index into the fabrics and incorporating large ideas for the homework exercises.

From the MOOC description:

Linear Algebra: Foundations to Frontiers (LAFF) is packed choked with tough, worthwhile fabric that's crucial for mathematicians, engineers, scientists, and an individual operating with huge datasets. scholars savor our new angle to educating linear algebra simply because: It’s visible. It connects hand calculations, mathematical abstractions, and desktop programming. It illustrates the advance of mathematical concept. It’s appropriate. during this path, you are going to study all of the average themes which are taught in common undergraduate linear algebra classes around the world, yet utilizing our designated procedure, you will additionally get extra! LAFF was once built following the syllabus of an introductory linear algebra path on the collage of Texas at Austin taught through Professor Robert van de Geijn, knowledgeable on excessive functionality linear algebra libraries. via brief movies, workouts, visualizations, and programming assignments, you are going to examine Vector and Matrix Operations, Linear ameliorations, fixing structures of Equations, Vector areas, Linear Least-Squares, and Eigenvalues and Eigenvectors. moreover, you'll get a glimpse of innovative examine at the improvement of linear algebra libraries, that are used all through computational technological know-how.

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Sample text

Week 1. 4 48 Summary of the Routines for Vector Operations Operation Abbrev. Definition Function Approx. 1 illustrates some special properties of the rotation. Functions with these properties are called called linear transformations. Thus, the illustrated rotation in 2D is an example of a linear transformation.

A library of vector-vector routines The functionality of the Python functions you will write is also part of the ”laff” library of routines. What this means will become obvious in subsequent units. Here is a table of all the vector functions, and the routines that implement them, that you will be able to use in future weeks is given in the following table: Week 1. Vectors in Linear Algebra Operation Abbrev. 34 Definition Function Approx. norm2( x ) 2n n Scaled addition (AXPY) y := αx + y Dot product (DOT) α := xT y Length (NORM 2) α := x 2 Next, let’s dive right in!

3 Programming without indices (dot product) as described in the video for this unit. Week 1. 17 Let α ∈ R, x, y ∈ Rn , and partition (Slice and Dice) these vectors as  x0   x1  x= .  ..  xN−1         and  y0   y1  y= .  ..  yN−1    ,   where xi , yi ∈ Rni with ∑N−1 i=0 ni = n. Then  x0   x1  αx + y = α  .  .. 5   y0     y1   + .   ..   yN−1  αx0 + y0        =     αx1 + y1 ..    . 6. 6 Programming without indices (axpy) as described in the video for this unit.

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