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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 .
The term R-matrix has several meanings, depending on the field of study.. The term R-matrix is used in connection with the Yang–Baxter equation, first introduced in the field of statistical mechanics in the works of J. B. McGuire in 1964 [1] and C. N. Yang in 1967 [2] and in the group algebra [] of the symmetric group in the work of A. A. Jucys in 1966.
In mathematics, every analytic function can be used for defining a matrix function that maps square matrices with complex entries to square matrices of the same size. This is used for defining the exponential of a matrix , which is involved in the closed-form solution of systems of linear differential equations .
In many cases, such a matrix R can be obtained by an explicit formula. Square roots that are not the all-zeros matrix come in pairs: if R is a square root of M, then −R is also a square root of M, since (−R)(−R) = (−1)(−1)(RR) = R 2 = M. A 2×2 matrix with two distinct nonzero eigenvalues has four square roots.
The set M(n, R) (also denoted M n (R) [7]) of all square n-by-n matrices over R is a ring called matrix ring, isomorphic to the endomorphism ring of the left R-module R n. [58] If the ring R is commutative , that is, its multiplication is commutative, then the ring M( n , R ) is also an associative algebra over R .
Decomposition: = where C is an m-by-r full column rank matrix and F is an r-by-n full row rank matrix Comment: The rank factorization can be used to compute the Moore–Penrose pseudoinverse of A , [ 2 ] which one can apply to obtain all solutions of the linear system A x = b {\displaystyle A\mathbf {x} =\mathbf {b} } .
In mathematics, matrix calculus is a specialized notation for doing multivariable calculus, especially over spaces of matrices.It collects the various partial derivatives of a single function with respect to many variables, and/or of a multivariate function with respect to a single variable, into vectors and matrices that can be treated as single entities.
SciPy adds a function scipy.linalg.pinv that uses a least-squares solver. The MASS package for R provides a calculation of the Moore–Penrose inverse through the ginv function. [24] The ginv function calculates a pseudoinverse using the singular value decomposition provided by the svd function in the base R package.