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[4]: 114 A DataFrame is a 2-dimensional data structure of rows and columns, similar to a spreadsheet, and analogous to a Python dictionary mapping column names (keys) to Series (values), with each Series sharing an index. [4]: 115 DataFrames can be concatenated together or "merged" on columns or indices in a manner similar to joins in SQL.
rank(A) = number of pivots in any echelon form of A, rank(A) = the maximum number of linearly independent rows or columns of A. [5] If the matrix represents a linear transformation, the column space of the matrix equals the image of this linear transformation. The column space of a matrix A is the set of all linear combinations of the columns in A.
Row labels are used to apply a filter to one or more rows that have to be shown in the pivot table. For instance, if the "Salesperson" field is dragged on this area then the other output table constructed will have values from the column "Salesperson", i.e., one will have a number of rows equal to the number of "Sales Person". There will also ...
Armadillo is C++ template library for linear algebra; includes various decompositions, factorisations, and statistics functions; its syntax is similar to MATLAB. Clojure with numeric libraries Neanderthal, ClojureCUDA, and ClojureCL to call optimized matrix and linear algebra functions on CPU and GPU.
This is an attempt to model or fit an equation line or curve to the data, such that Y is a function of X. [74] [75] Necessary condition analysis (NCA) may be used when the analyst is trying to determine the extent to which independent variable X allows variable Y (e.g., "To what extent is a certain unemployment rate (X) necessary for a certain ...
The first American-made pocket-sized calculator, the Bowmar 901B (popularly termed The Bowmar Brain), measuring 5.2 by 3.0 by 1.5 inches (132 mm × 76 mm × 38 mm), came out in the Autumn of 1971, with four functions and an eight-digit red LED display, for US$240, while in August 1972 the four-function Sinclair Executive became the first ...
Multiplying a row by a number multiplies the determinant by this number. Adding a multiple of one row to another row does not change the determinant. The above properties relating to rows (properties 2–4) may be replaced by the corresponding statements with respect to columns. The determinant is invariant under matrix similarity.
The five-number summary gives information about the location (from the median), spread (from the quartiles) and range (from the sample minimum and maximum) of the observations. Since it reports order statistics (rather than, say, the mean) the five-number summary is appropriate for ordinal measurements, as well as interval and ratio measurements.