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dplyr is an R package whose set of functions are designed to enable dataframe (a spreadsheet-like data structure) manipulation in an intuitive, user-friendly way. It is one of the core packages of the popular tidyverse set of packages in the R programming language. [1]
Animation of Gaussian elimination. Red row eliminates the following rows, green rows change their order. In mathematics, Gaussian elimination, also known as row reduction, is an algorithm for solving systems of linear equations. It consists of a sequence of row-wise operations performed on the corresponding matrix of coefficients.
A matrix is in reduced row echelon form if it is in row echelon form, with the additional property that the first nonzero entry of each row is equal to and is the only nonzero entry of its column. The reduced row echelon form of a matrix is unique and does not depend on the sequence of elementary row operations used to obtain it.
If we did not swap rows at all during this process, we can perform the row operations simultaneously for each column by setting ():= (), where is the N × N identity matrix with its n-th column replaced by the transposed vector (+,,).
37.5 million image-text examples with 11.5 million unique images across 108 Wikipedia languages. 11,500,000 image, caption Pretraining, image captioning 2021 [7] Srinivasan e al, Google Research Visual Genome Images and their description 108,000 images, text Image captioning 2016 [8] R. Krishna et al. Berkeley 3-D Object Dataset
Unique constraint. A unique constraint can be defined on columns that allow nulls, in which case rows that include nulls may not actually be unique across the set of columns defined by the constraint. Each table can have multiple unique constraints. On some RDBMS a unique constraint generates a nonclustered index by default.
The QR decomposition via Givens rotations is the most involved to implement, as the ordering of the rows required to fully exploit the algorithm is not trivial to determine. However, it has a significant advantage in that each new zero element affects only the row with the element to be zeroed (i) and a row above (j). This makes the Givens ...
A row consists of 1, a, a 2, a 3, etc., and each row uses a different variable. Walsh matrix: A square matrix, with dimensions a power of 2, the entries of which are +1 or −1, and the property that the dot product of any two distinct rows (or columns) is zero. Z-matrix: A matrix with all off-diagonal entries less than zero.