I just saw this paper recently which mentioned that the optimization on a Grassmanian Manifold can be used to get an achieve an best approximation of a multilinear rank of a tensor (in the sense of a multidimensional matrix, also called a hypermatrix). Does anyone happen to know what Grassmanians have to do with tensors and their analysis? And where could I learn more about Grassmanian manifolds (enough to understand the use here, more is of course welcome =)


The paper is here for those interested
[Paper](http://www.stanford.edu/~lekheng/jobs/qn.pdf)


(I hope this isn't too specific)



Algebraic Geometry in an applied setting?
You might also want to check out  [this](http://www.math.tamu.edu/~jml/rankvsbrank.pdf)  paper by Landsberg and Teitler on getting bounds for the Waring rank (and border rank) of symmetric tensors using geometry.


The point here is that the projective bundle on a vector space captures the geometry of its symmetric tensors so one can reformulate questions about say the rank into questions about the geometry of secant varieties on the projective bundle of interest. It turns out one can prove some new bounds using some very classical algebraic geometry.


