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# SparseArray

 SparseArray[{pos1->val1, pos2->val2, ...}] yields a sparse array in which values vali appear at positions posi. SparseArray[{pos1, pos2, ...}->{val1, val2, ...}] yields the same sparse array. SparseArray[list] yields a sparse array version of list. SparseArray[data, {d1, d2, ...}]yields a sparse array representing a d1d2... array. SparseArray[data, dims, val]yields a sparse array in which unspecified elements are taken to have value val.
• By default, SparseArray takes unspecified elements to be 0.
• Normal[SparseArray[...]] gives the ordinary array corresponding to a sparse array object.
• ArrayRules[SparseArray[...]] gives the list of rules {pos1->val1, pos2->val2, ...}.
• The position specifications posi can contain patterns.
• SparseArray[{{i_, i_}->1}, {d, d}] gives a dd identity matrix.
• Rules of the form Band[...]->vals specify values on bands in the sparse array.
• With rules posi:>vali the vali are evaluated separately for each set of indices that match posi.
• SparseArray[list] requires that list be a full array, with all parts at a particular level being lists of the same length.
• The individual elements of a sparse array cannot themselves be lists.
• SparseArray[rules] yields a sparse array with dimensions exactly large enough to include elements whose positions have been explicitly specified.
• List and matrix operations are typically set up to work as they do on Normal[SparseArray[...]].
• Functions with attribute Listable are automatically threaded over the individual elements of the ordinary arrays represented by SparseArray objects.
• Part extracts specified parts of the array represented by a SparseArray object, rather than parts of the SparseArray expression itself.
• Functions like Map are automatically applied to components in a SparseArray object.
• SparseArray is treated as a raw object by functions like AtomQ, and for purposes of pattern matching.
• Dimensions gives the dimensions of a sparse array.
• The standard output format for a sparse array indicates the number of non-default elements and the total dimensions.
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