Friday, 8 August 2014

linear algebra - What is the matrix property, 'hollowness'?



In a paper on Euclidean distance matrices, I encountered a reference to 'hollowness' as a matrix property. It was mentioned in the same breath as other properties that I am familiar with: symmetry, etc. I can't find any reference to hollowness in any of my linear algebra texts, through Google searches or anything else, so I'm stuck. Does anyone know what hollowness is, with regard to matrix properties?



Answer



From the article itself:




zero-diagonal (or hollow)




Then checking Hollow matrix on Wikipedia,





a hollow matrix may refer to one of several related classes of matrix,




These classes are:




  • Sparse matrices,

  • Matrices with diagonal entries all zero, or

  • Matrices with a block of zeroes.




The text seems to be indicating that the second definition is what we want. Of course this is an obvious property of a distance matrix, since the distance from a point to itself is zero.


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