By Robert van de Geijn, Maggie Myers
LAFF all started as an important Open on-line path (MOOC) funded partially by means of the college of Texas approach and the nationwide technological know-how starting place (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 least summer season 2014.
The "Notes to LAFF With" are a PDF ebook that turns into the "hub" by which the opposite LAFF fabric (e.g., the movies) could be accessed. It is going past the notes that have been published as a part of the edX MOOC through additionally offering an index into the fabrics and incorporating broad suggestions for the homework exercises.
From the MOOC description:
Linear Algebra: Foundations to Frontiers (LAFF) is packed packed with demanding, profitable fabric that's crucial for mathematicians, engineers, scientists, and a person operating with huge datasets. scholars take pleasure in our special approach to instructing linear algebra simply because: It’s visible. It connects hand calculations, mathematical abstractions, and laptop programming. It illustrates the improvement of mathematical concept. It’s appropriate. during this path, you are going to research all of the ordinary themes which are taught in commonplace undergraduate linear algebra classes around the globe, yet utilizing our special procedure, you are going to additionally get extra! LAFF was once constructed following the syllabus of an introductory linear algebra direction on the college of Texas at Austin taught by means of Professor Robert van de Geijn, knowledgeable on excessive functionality linear algebra libraries. via brief video clips, workouts, visualizations, and programming assignments, you'll learn Vector and Matrix Operations, Linear adjustments, fixing platforms of Equations, Vector areas, Linear Least-Squares, and Eigenvalues and Eigenvectors. furthermore, you'll get a glimpse of leading edge learn at the improvement of linear algebra libraries, that are used all through computational technological know-how.
Download it at no cost: http://www.ulaff.net/
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Additional info for LAFF - Linear Algebra: Foundations to Frontiers
2 Let x ∈ Rn . The length of x is less than zero: x < 0. 3 If x is a unit vector then x is a unit basis vector. 4 If x is a unit basis vector then x is a unit vector. 5 If x and y are perpendicular (orthogonal) then xT y = 0. TRUE/FALSE Hint: Consider the picture x+y x y ☛ SEE ANSWER Week 1. 6 Let x, y ∈ Rn be nonzero vectors and let the angle between them equal θ. Then xT y . cos θ = x 2 y 2 Always/Sometimes/Never Hint: Consider the picture and the “Law of Cosines” that you learned in high school.
N − 1 w := χ j v j + w endfor The axpy operation computed y := αx + y. In our algorithm, χ j takes the place of α, v j the place of x, and w the place of y. Cost We noted that computing w = χ0 v0 +χ1 v1 +· · · χn−1 vn−1 can be implementated as n AXPY operations. This suggests that the cost is n times the cost of an AXPY operation with vectors of size m: n × (2m) = 2mn flops and (approximately) n × (3m) memops. However, one can actually do better. The vector w is updated repeatedly. If this vector stays in the L1 cache of a computer, then it needs not be repeatedly loaded from memory, and the cost becomes m memops (to load w into the cache) and then for each AXPY operation (approximately) m memops (to read v j (ignoring the cost of reading χ j ).
This provides an interactive environment in which we can intersperse text with executable code. 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.