Finding singular values and norms of matrices. The singular values of a matrix m are the square roots of the eigenvalues of m.m^*, where * denotes Hermitian transpose. The ...

A typical Mathematica notebook containing text, graphics, and Mathematica expressions. The brackets on the right indicate the extent of each cell. Mathematica notebooks are ...

The main expression or object that a built-in Mathematica function acts on is given as the first argument to the function. As part of the syntax, a built-in Mathematica ...

Mathematica integrates many aspects of statistical data analysis, from getting and exploring data to building high-quality models and and deducing consequences. Mathematica ...

NSum[f, {i, i_min, i_max}] gives a numerical approximation to the sum \[Sum]i = i_min i_max f.NSum[f, {i, i_min, i_max, di}] uses a step di in the sum.

LiftingWaveletTransform[data] gives the lifting wavelet transform (LWT) of an array of data.LiftingWaveletTransform[data, wave] gives the lifting wavelet transform using the ...

There are many situations where one wants to find a formula that best fits a given set of data. One way to do this in Mathematica is to use Fit. Basic linear fitting. Here is ...

The way modules work in Mathematica is basically very simple. Every time any module is used, a new symbol is created to represent each of its local variables. The new symbol ...

Applying transformation rules. The replacement operator /. (pronounced "slash-dot") applies rules to expressions. You can give a list of rules to apply. Each rule will be ...

Here is one way to get multiple minima: call NMinimize multiple times with different random seeds, which will cause different optimization paths to be taken. This defines a ...