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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. If A = [a 1 ⋯ a n], then colsp(A) = span({a 1 ...
Synonym for binary matrix or logical matrix. Alternant matrix: A matrix in which successive columns have a particular function applied to their entries. Alternating sign matrix: A square matrix with entries 0, 1 and −1 such that the sum of each row and column is 1 and the nonzero entries in each row and column alternate in sign. Anti-diagonal ...
In linear algebra, a column vector with elements is an matrix [1] consisting of a single column of entries, for example, = [].. Similarly, a row vector is a matrix for some , consisting of a single row of entries, = […]. (Throughout this article, boldface is used for both row and column vectors.)
RStudio IDE (or RStudio) is an integrated development environment for R, a programming language for statistical computing and graphics. It is available in two formats: RStudio Desktop is a regular desktop application while RStudio Server runs on a remote server and allows accessing RStudio using a web browser.
While the terms allude to the rows and columns of a two-dimensional array, i.e. a matrix, the orders can be generalized to arrays of any dimension by noting that the terms row-major and column-major are equivalent to lexicographic and colexicographic orders, respectively. It is also worth noting that matrices, being commonly represented as ...
R is a programming language for statistical computing and data visualization. It has been adopted in the fields of data mining, bioinformatics and data analysis. [9] The core R language is augmented by a large number of extension packages, containing reusable code, documentation, and sample data. R software is open-source and free software.
B i consists of n block matrices of size m × m, stacked column-wise, and all these matrices are all-zero except for the i-th one, which is a m × m identity matrix I m. Then the vectorized version of X can be expressed as follows: vec ( X ) = ∑ i = 1 n B i X e i {\displaystyle \operatorname {vec} (\mathbf {X} )=\sum _{i=1}^{n}\mathbf {B ...
The design matrix has dimension n-by-p, where n is the number of samples observed, and p is the number of variables measured in all samples. [4] [5]In this representation different rows typically represent different repetitions of an experiment, while columns represent different types of data (say, the results from particular probes).