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I've been reading up on papers in scientific computation that utilize terms such as "Stiefel manifold" and "Grassmannian" that seem to be invoked in numerical linear algebra. I don't have any background in manifolds nor in topology (except for the one needed for real analysis) but I'd like to read up more to learn about 1) manifolds in general and 2) the relevant concepts used in numerical linear algebra.

I was initially planning on starting with Loring Tu's book "Introduction to manifolds" and perhaps continue with John Lee's "Introduction to smooth manifolds" book if there is interest. However, a quick search through the book reveals that "Stiefel manifold" does not exist. As someone who does not know anything about this field, should this be surprising?

I guess my question really is: What book on manifold is suited for self study if your application is in numerical linear algebra? My topological background is only at the real analysis level. Or is Loring Tu's book sufficient just to know how manifolds operate? If so, what are the chapters I can skip?

Appreciate the suggestions. Thanks!

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