Matrix inversion. Here is a simple 2×2 matrix. This gives the inverse of m. In producing this formula, Mathematica implicitly assumes that the determinant ad-bc is nonzero.

Mathematica uses a large number of original algorithms to provide automatic systemwide support for inequalities and inequality constraints. Whereas equations can often be ...

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Booleans represents the domain of Booleans, as in x \[Element] Booleans.

To begin, consider an initial value problem for a linear first-order ODE. This is a linear first-order ODE. Notice that the general solution is a linear function of the ...

The differential equations that arise in modern applications often have discontinuous coefficients. DSolve can handle a wide variety of such ODEs with piecewise coefficients. ...

Supporting a large number of numerical integration methods for differential equations is a lot of work. In order to cut down on maintenance and duplication of code, common ...

The essence of most methods is in the local quadratic model that is used to determine the next step. The FindMinimum function in Mathematica has five essentially different ...

[AN96] Adams, L. and J. L. Nazareth. (Eds.) Linear and Nonlinear Conjugate Gradient-Related Methods. SIAM, 1996. [Br02] Brent, R. P. Algorithms for Minimization without ...

Mathematically, sufficient conditions for a local minimum of a smooth function are quite straightforward: x^* is a local minimum if ∇f(x^*)=0 and the Hessian ∇^2f(x^*) is ...