On linear-algebraic notions of expansion

  title={On linear-algebraic notions of expansion},
  author={Yinan Li and Y C Qiao and A Wigderson and Yuval Wigderson and Chuan-Hai Zhang},
  journal={Electron. Colloquium Comput. Complex.},
A fundamental fact about bounded-degree graph expanders is that three notions of expansion -- vertex expansion, edge expansion, and spectral expansion -- are all equivalent. In this paper, we study to what extent such a statement is true for linear-algebraic notions of expansion. There are two well-studied notions of linear-algebraic expansion, namely dimension expansion (defined in analogy to graph vertex expansion) and quantum expansion (defined in analogy to graph spectral expansion… 

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