Go backward to Linear Vector of Values Go up to Top Go forward to Multidimensional Arrays

Multidimensional Arrays

• Array may contain other arrays.

  Three-dimensional array is vector whose components are two-dimensional vectors.

• Hierarchy of arrays defined as infinite sum
  • 1DArray = (Index -> Location) x Index x Index.
  • (n+1)DArray = (Index -> nDArray) x Index x Index.

  a in MDArray = Sum_m=1^oo mDArray
  = ((Index -> Location) x Index x Index)
  + ((Index -> ((Index -> Location) x Index x Index)) x Index x Index)
  + ((Index -> ((Index -> ((Index -> Location) x Index x Index)) x Index x Index)) x Index x Index) + ...

• 1DArray maps indices to locations, 2DArray maps indices to 1D arrays, ....