ObservabilityGramian[ss] gives the observability Gramian of the StateSpaceModel object ss.

StringReplaceList["string", s -> sp] or StringReplaceList["string", {s_1 -> sp_1, s_2 -> sp_2, ...}] gives a list of the strings obtained by replacing each individual ...

Take[list, n] gives the first n elements of list. Take[list, -n] gives the last n elements of list. Take[list, {m, n}] gives elements m through n of list. Take[list, seq_1, ...

Many programs you write will involve operations that need to be iterated several times. Nest and NestList are powerful constructs for doing this. Applying functions of one ...

Modules in Mathematica allow you to treat the names of variables as local. Sometimes, however, you want the names to be global, but values to be local. You can do this in ...

Eigenvalues and eigenvectors. The eigenvalues of a matrix m are the values λ_i for which one can find nonzero vectors v_i such that m.v_i λ_iv_i. The eigenvectors are the ...

Functions for creating power series. Here is the power series expansion for exp(x) about the point x0 to order x^4. Here is the series expansion of exp(x) about the point ...

Since lists are just a particular kind of expression, it will come as no surprise that you can refer to parts of any expression much as you refer to parts of a list. This ...

"Sound" describes how you can take functions and lists of data and produce sounds from them. Here we discuss how sounds are represented in Mathematica. Mathematica treats ...

Functionality in this package has been added to the built-in Mathematica kernel. CumulativeSums is replaced by Accumulate. Frequencies is replaced by Tally. BinCounts and ...