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[4]: 136 A DataFrame's column names are stored and implemented identically to an index. As such, a DataFrame can be thought of as having two indices: one column-based and one row-based. Because column names are stored as an index, these are not required to be unique. [9]: 103–105 If data is a Series, then data['a'] returns all values with the ...
For a square matrix, the diagonal (or main diagonal or principal diagonal) is the diagonal line of entries running from the top-left corner to the bottom-right corner. [ 1 ] [ 2 ] [ 3 ] For a matrix A {\displaystyle A} with row index specified by i {\displaystyle i} and column index specified by j {\displaystyle j} , these would be entries A i ...
Even though the row is indicated by the first index and the column by the second index, no grouping order between the dimensions is implied by this. The choice of how to group and order the indices, either by row-major or column-major methods, is thus a matter of convention. The same terminology can be applied to even higher dimensional arrays.
A vector treated as an array of numbers by writing as a row vector or column vector (whichever is used depends on convenience or context): = (), = Index notation allows indication of the elements of the array by simply writing a i, where the index i is known to run from 1 to n, because of n-dimensions. [1]
A dense index in databases is a file with pairs of keys and pointers for every record in the data file. Every key in this file is associated with a particular pointer to a record in the sorted data file. In clustered indices with duplicate keys, the dense index points to the first record with that key. [3]
Here is an implementation which utilizes the fold-left function. reverseMap f = foldl ( \ ys x -> f x : ys ) [] Since reversing a singly linked list is also tail-recursive, reverse and reverse-map can be composed to perform normal map in a tail-recursive way, though it requires performing two passes over the list.
For a (0,2) tensor, [1] twice contracting with the inverse metric tensor and contracting in different indices raises each index: =. Similarly, twice contracting with the metric tensor and contracting in different indices lowers each index:
Discussing possible designs of array ranges by enclosing them in a chained inequality, combining sharp and standard inequalities to four possibilities, demonstrating that to his conviction zero-based arrays are best represented by non-overlapping index ranges, which start at zero, alluding to open, half-open and closed intervals as with the ...