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SymPy is an open-source Python library for symbolic computation. It provides computer algebra capabilities either as a standalone application, as a library to other applications, or live on the web as SymPy Live [2] or SymPy Gamma. [3] SymPy is simple to install and to inspect because it is written entirely in Python with few dependencies.
In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance from the origin: it commutes with scaling, obeys a form of the triangle inequality, and is zero only at the origin.
Provides tools for solving and manipulating symbolic math expressions and performing variable-precision arithmetic. SymPy: Ondřej Čertík 2006 2007 1.13.2: 11 August 2024: Free modified BSD license: Python-based TI-Nspire CAS (Computer Software) Texas Instruments: 2006 2009 5.1.3: 2020 Proprietary: Successor to Derive.
Eigen is a vector mathematics library with performance comparable with Intel's Math Kernel Library; Hermes Project: C++/Python library for rapid prototyping of space- and space-time adaptive hp-FEM solvers. IML++ is a C++ library for solving linear systems of equations, capable of dealing with dense, sparse, and distributed matrices. IT++ is a ...
In mathematics, the operator norm measures the "size" of certain linear operators by assigning each a real number called its operator norm. Formally, it is a norm defined on the space of bounded linear operators between two given normed vector spaces .
With the SymPy symbolic library, multiplication of array objects as either a*b or a@b will produce the matrix product. The Hadamard product can be obtained with the method call a.multiply_elementwise(b). [22] Some Python packages include support for Hadamard powers using methods like np.power(a, b), or the Pandas method a.pow(b).
In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1. A unit vector is often denoted by a lowercase letter with a circumflex, or "hat", as in ^ (pronounced "v-hat"). The normalized vector û of a non-zero vector u is the unit vector in the direction of u, i.e.,
Suppose a vector norm ‖ ‖ on and a vector norm ‖ ‖ on are given. Any matrix A induces a linear operator from to with respect to the standard basis, and one defines the corresponding induced norm or operator norm or subordinate norm on the space of all matrices as follows: ‖ ‖, = {‖ ‖: ‖ ‖ =} = {‖ ‖ ‖ ‖:} . where denotes the supremum.