Many large-scale applications of linear algebra involve matrices that have many elements, but comparatively few that are nonzero. You can represent such sparse matrices ...

Mathematica routinely handles huge arrays of numeric, symbolic, textual, or any other data, with any dimension or structure. Arrays are fully integrated into Mathematica's ...

Here is a system of two ODEs whose coefficient matrix has real and distinct eigenvalues. This solves the system. Note that the general solution depends on two arbitrary ...

While there is typically one representation for exact numbers, approximate numbers can be presented differently according to the conventions of different professions or ...

FullSimplify[expr] tries a wide range of transformations on expr involving elementary and special functions, and returns the simplest form it finds. FullSimplify[expr, assum] ...

The simplest way to mix text and formulas in a Mathematica notebook is to put each kind of material in a separate cell. Sometimes, however, you may want to embed a formula ...

The general form of an ODE with order n is As in the case of second-order ODEs, such an ODE can be classified as linear or nonlinear. The general form of a linear ODE of ...

RSolve[eqn, a[n], n] solves a recurrence equation for a[n]. RSolve[{eqn_1, eqn_2, ...}, {a_1[n], a_2[n], ...}, n] solves a system of recurrence equations. RSolve[eqn, a[n_1, ...

Converting from strings or boxes to expressions. This takes a string and interprets it as an expression. Here is the box structure corresponding to the textual form of an ...

Not only can Mathematica perform very complicated data analysis, it can also display these results in a formatted, easy-to-read display that can be used in other documents or ...