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NumPy (pronounced / ˈ n ʌ m p aɪ / NUM-py) is a library for the Python programming language, adding support for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays. [3]
An array data structure can be mathematically modeled as an abstract data structure (an abstract array) with two operations get(A, I): the data stored in the element of the array A whose indices are the integer tuple I. set(A, I, V): the array that results by setting the value of that element to V. These operations are required to satisfy the ...
One of the reasons for the importance of the matrix exponential is that it can be used to solve systems of linear ordinary differential equations.The solution of = (), =, where A is a constant matrix and y is a column vector, is given by =.
In addition to support for vectorized arithmetic and relational operations, these languages also vectorize common mathematical functions such as sine. For example, if x is an array, then y = sin (x) will result in an array y whose elements are sine of the corresponding elements of the array x. Vectorized index operations are also supported.
In array languages, operations are generalized to apply to both scalars and arrays. Thus, a+b expresses the sum of two scalars if a and b are scalars, or the sum of two arrays if they are arrays. An array language simplifies programming but possibly at a cost known as the abstraction penalty.
In numerical linear algebra, the Arnoldi iteration is an eigenvalue algorithm and an important example of an iterative method.Arnoldi finds an approximation to the eigenvalues and eigenvectors of general (possibly non-Hermitian) matrices by constructing an orthonormal basis of the Krylov subspace, which makes it particularly useful when dealing with large sparse matrices.
In mathematics, an anti-diagonal matrix is a square matrix where all the entries are zero except those on the diagonal going from the lower left corner to the upper right corner (↗), known as the anti-diagonal (sometimes Harrison diagonal, secondary diagonal, trailing diagonal, minor diagonal, off diagonal or bad diagonal).
Given three matrices A, B and C, the products (AB)C and A(BC) are defined if and only if the number of columns of A equals the number of rows of B, and the number of columns of B equals the number of rows of C (in particular, if one of the products is defined, then the