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About Singular Simplex

  1. Apr 20, 2010 #1
    Why do we use the term "singular" to describe singular simplex? Are there any relations between singular matrix (or singular point)and singular simplex?
     
  2. jcsd
  3. Apr 20, 2010 #2

    quasar987

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    I ran a google search for singular and found http://www.thefreedictionary.com/singular. Definitions 3 and 4 read

    3. Being beyond what is ordinary or usual; remarkable.
    4. Deviating from the usual or expected; odd. See Synonyms at strange.

    and I believe it is the meaning appropriate for "singular simplex". Indeed, whereas in simplicial homology, the objects of interest are actual simplices (the n-dimensional generalisation of a triangle), in singular homology, the objects of interest are merely continuous images of simplices. In particular, these images may be very degenerate (a point for instance) and not resemble a simplex at all. That is, they may deviate from what is expected of something called a simplex.
     
  4. Apr 21, 2010 #3
    To answer the other question, singular matrices and singular simplices have nothing to do with each other, unless you really stretch :)

    (The big stretch: if you have a degenerate simplex in the top dimension represented by a differentiable map, its Jacobian would be singular)
     
  5. Apr 22, 2010 #4
    Thank for your replies.
     
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