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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.
The transpose (indicated by T) of any row vector is a column vector, and the transpose of any column vector is a row vector: […] = [] and [] = […]. The set of all row vectors with n entries in a given field (such as the real numbers ) forms an n -dimensional vector space ; similarly, the set of all column vectors with m entries forms an m ...
More generally, there are d! possible orders for a given array, one for each permutation of dimensions (with row-major and column-order just 2 special cases), although the lists of stride values are not necessarily permutations of each other, e.g., in the 2-by-3 example above, the strides are (3,1) for row-major and (1,2) for column-major.
There is a similar notion of column equivalence, defined by elementary column operations; two matrices are column equivalent if and only if their transpose matrices are row equivalent. Two rectangular matrices that can be converted into one another allowing both elementary row and column operations are called simply equivalent .
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1. All of these words sound like a specific letter in the alphabet. 2. These items are known for their notched edges. 3. Expressions that show mild frustration. 4. Features of a flowing body of water.
Within two hours of the initial quake, the area had experienced 13 different aftershocks, ranging from 5.1 to 3.1, according to the U.S. Geological Survey. 👉 Here's everything we know.
Santiago Felipe/Getty, Giles Keyte/Universal Pictures 'Wicked' director Jon M. Chu; 'Wicked' stars Cynthia Erivo and Ariana Grande