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How is this "advanced" linear algebra? This was all covered my freshman linear algebra course.

flor1s 7y ago
I take it they will go deeper into the materials than they went in their previous course (http://www.ulaff.net http://www.ulaff.net), which also covered the topics to a limited extend.
geoalchimista 7y ago
Don't know why you are downvoted but I second your opinion. The contents listed here seem to emphasize applications in CS rather than theoretical aspects (e.g., Hilbert space, tensors, spectral theory).
enthdegree 7y ago
ime most introductory linear algebra classes do not affect students to develop a robust mental model of the fundamental theorem of linear algebra. the first picture in the course description is this very model, so ideally this class does that. i hope...
ivan_ah 7y ago
It's the same topics as first-year linear algebra, but now done "for real" using algorithms that scale. Part I: SVD = bread and butter in industry with lots of applications in ML and stats, engineering stuff too, see https://www.youtube.com/watch?v=R9UoFyqJca8 https://www.youtube.com/watch?v=R9UoFyqJca8 ) Part II: Solving Linear Systems = 70% of science can be describes as A*x=b where A is a matrix and x and b are vectors. Spoiler alert: the "find the RREF algorithm" that we learn in first-year LA is not the most efficient (or numerically stable) option. Part III: Eigenvalues "for real" this time = e.g. iterative solution methods that scale. The flagship application of this idea would be the initial PageRank algorithm that works on the adjacecy matrix representaiton of the graph of all webpages (millions of columns, see http://infolab.stanford.edu/pub/papers/google.pdf http://infolab.stanford.edu/pub/papers/google.pdf ) So to summarize, this course covers all kinds of topics that you don't need to know if you want to apply LA to small and medium data, but for large scale stuff would be really good to know.
- Myrmornis 7y ago
  I don't think that it is helpful to classify basic vs advanced linear algebra according to whether the techniques "scale" to larger data sets. Linear algebra isn't necessarily about data sets at all. Many of these courses (even this "advanced" one it looks like) completely fail to convey the understanding that vectors and linear transformations on finite-dimensional vector spaces only acquire numerical representations as numerical vectors and matrices when a basis is specified; but that should be part of a basic linear algebra course.
FabHK 7y ago
"Applied" or "Numerical" LA would be better descriptors, yes.

I take it they will go deeper into the materials than they went in their previous course (http://www.ulaff.net http://www.ulaff.net), which also covered the topics to a limited extend.

geoalchimista 7y ago

Don't know why you are downvoted but I second your opinion. The contents listed here seem to emphasize applications in CS rather than theoretical aspects (e.g., Hilbert space, tensors, spectral theory).

enthdegree 7y ago

ime most introductory linear algebra classes do not affect students to develop a robust mental model of the fundamental theorem of linear algebra. the first picture in the course description is this very model, so ideally this class does that. i hope...

ivan_ah 7y ago

It's the same topics as first-year linear algebra, but now done "for real" using algorithms that scale. Part I: SVD = bread and butter in industry with lots of applications in ML and stats, engineering stuff too, see https://www.youtube.com/watch?v=R9UoFyqJca8 https://www.youtube.com/watch?v=R9UoFyqJca8 ) Part II: Solving Linear Systems = 70% of science can be describes as A*x=b where A is a matrix and x and b are vectors. Spoiler alert: the "find the RREF algorithm" that we learn in first-year LA is not the most efficient (or numerically stable) option. Part III: Eigenvalues "for real" this time = e.g. iterative solution methods that scale. The flagship application of this idea would be the initial PageRank algorithm that works on the adjacecy matrix representaiton of the graph of all webpages (millions of columns, see http://infolab.stanford.edu/pub/papers/google.pdf http://infolab.stanford.edu/pub/papers/google.pdf ) So to summarize, this course covers all kinds of topics that you don't need to know if you want to apply LA to small and medium data, but for large scale stuff would be really good to know.

Myrmornis 7y ago
I don't think that it is helpful to classify basic vs advanced linear algebra according to whether the techniques "scale" to larger data sets. Linear algebra isn't necessarily about data sets at all. Many of these courses (even this "advanced" one it looks like) completely fail to convey the understanding that vectors and linear transformations on finite-dimensional vector spaces only acquire numerical representations as numerical vectors and matrices when a basis is specified; but that should be part of a basic linear algebra course.

FabHK 7y ago

"Applied" or "Numerical" LA would be better descriptors, yes.