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Pandas (styled as pandas) is a software library written for the Python programming language for data manipulation and analysis. In particular, it offers data structures and operations for manipulating numerical tables and time series .
Google Sheets is a spreadsheet application and part of the free, web-based Google Docs Editors suite offered by Google. Google Sheets is available as a web application; a mobile app for: Android, iOS, and as a desktop application on Google's ChromeOS. The app is compatible with Microsoft Excel file formats. [5]
In linear algebra, the transpose of a matrix is an operator which flips a matrix over its diagonal; that is, it switches the row and column indices of the matrix A by producing another matrix, often denoted by A T (among other notations). [1] The transpose of a matrix was introduced in 1858 by the British mathematician Arthur Cayley. [2]
The conjugate transpose of a matrix with real entries reduces to the transpose of , as the conjugate of a real number is the number itself. The conjugate transpose can be motivated by noting that complex numbers can be usefully represented by 2 × 2 {\displaystyle 2\times 2} real matrices, obeying matrix addition and multiplication: a + i b ≡ ...
A graph and its transpose. In the mathematical and algorithmic study of graph theory, the converse, [1] transpose [2] or reverse [3] of a directed graph G is another directed graph on the same set of vertices with all of the edges reversed compared to the orientation of the corresponding edges in G.
A bacterial DNA transposon. A transposable element (TE), also transposon, or jumping gene, is a type of mobile genetic element, a nucleic acid sequence in DNA that can change its position within a genome, sometimes creating or reversing mutations and altering the cell's genetic identity and genome size.
Some instruments are constructed in a variety of sizes, with the larger versions having a lower range than the smaller ones. Common examples are clarinets (the high E ♭ clarinet, soprano instruments in C, B ♭ and A, the alto in E ♭, and the bass in B ♭), flutes (the piccolo, transposing at the octave, the standard concert-pitch flute, and the alto flute in G), saxophones (in several ...
Secondly, in the classical approach to differential geometry, it is not bases of the tangent bundle that are the most primitive object, but rather changes in the coordinate system. Vectors with contravariant components transform in the same way as changes in the coordinates (because these actually change oppositely to the induced change of basis).