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Matrix Toolkit Java is a linear algebra library based on BLAS and LAPACK. ojAlgo is an open source Java library for mathematics, linear algebra and optimisation. exp4j is a small Java library for evaluation of mathematical expressions. SuanShu is an open-source Java math library. It supports numerical analysis, statistics and optimization.
Matrix Toolkit Java (MTJ) is an open-source Java software library for performing numerical linear algebra. The library contains a full set of standard linear algebra operations for dense matrices based on BLAS and LAPACK code. Partial set of sparse operations is provided through the Templates project.
Wolfram Mathematica is a software system with built-in libraries for several areas of technical computing that allows machine learning, statistics, symbolic computation, data manipulation, network analysis, time series analysis, NLP, optimization, plotting functions and various types of data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in ...
The kernel of a m × n matrix A over a field K is a linear subspace of K n. That is, the kernel of A, the set Null(A), has the following three properties: Null(A) always contains the zero vector, since A0 = 0. If x ∈ Null(A) and y ∈ Null(A), then x + y ∈ Null(A). This follows from the distributivity of matrix multiplication over addition.
The following tables provide a comparison of computer algebra systems (CAS). [1] [2] [3] A CAS is a package comprising a set of algorithms for performing symbolic manipulations on algebraic objects, a language to implement them, and an environment in which to use the language.
Theoretically, a Gram matrix with respect to {, …,} (sometimes also called a "kernel matrix" [4]), where = (,), must be positive semi-definite (PSD). [5] Empirically, for machine learning heuristics, choices of a function k {\displaystyle k} that do not satisfy Mercer's condition may still perform reasonably if k {\displaystyle k} at least ...
SuanShu is a Java math library. It is open-source under Apache License 2.0 available in GitHub. SuanShu is a large collection of Java classes for basic numerical analysis, statistics, and optimization. [1] It implements a parallel version of the adaptive strassen's algorithm for fast matrix multiplication. [2]
The project's webpage contains the following statement, "(JAMA) is no longer actively developed to keep track of evolving usage patterns in the Java language, nor to further improve the API. We will, however, fix outright errors in the code." [3] The last bug fix was released November 2012, with the previous one being released in 2005.