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In 493 AD, Victorius of Aquitaine wrote a 98-column multiplication table which gave (in Roman numerals) the product of every number from 2 to 50 times and the rows were "a list of numbers starting with one thousand, descending by hundreds to one hundred, then descending by tens to ten, then by ones to one, and then the fractions down to 1/144 ...
2008 Excel 12.0 (part of Office 2008) 2010 Excel 14.0 (part of Office 2011) 2015 Excel 15.0 (part of Office 2016—Office 2016 for Mac brings the Mac version much closer to parity with its Windows cousin, harmonizing many of the reporting and high-level developer functions, while bringing the ribbon and styling into line with its PC counterpart ...
Column labels are used to apply a filter to one or more columns that have to be shown in the pivot table. For instance if the "Salesperson" field is dragged to this area, then the table constructed will have values from the column "Sales Person", i.e., one will have a number of columns equal to the number of "Salesperson". There will also be ...
Thus A T x = 0 if and only if x is orthogonal (perpendicular) to each of the column vectors of A. It follows that the left null space (the null space of A T) is the orthogonal complement to the column space of A. For a matrix A, the column space, row space, null space, and left null space are sometimes referred to as the four fundamental subspaces.
where I is the identity matrix of dimension equal to the rank of the entire matrix, X is a matrix with rows and columns, and the two 0 's are zero matrices of appropriate size. Since a permutation of columns is not a row operation, the resulting matrix is inequivalent under elementary row operations.
A cube is not a "cube" in the strict mathematical sense, as the sides are not all necessarily equal. But this term is used widely. A Slice is a term for a subset of the data, generated by picking a value for one dimension and only showing the data for that value (for instance only the data at one point in time). Spreadsheets are only 2 ...
For example, CSC is (val, row_ind, col_ptr), where val is an array of the (top-to-bottom, then left-to-right) non-zero values of the matrix; row_ind is the row indices corresponding to the values; and, col_ptr is the list of val indexes where each column starts. The name is based on the fact that column index information is compressed relative ...
Posting is the process of recording amounts as credits (right side), and amounts as debits (left side), in the pages of the general ledger. Additional columns to the right hold a running activity total (similar to a chequebook). [9] The general ledger should include the date, description and balance or total amount for each account.