Norm[expr] gives the norm of a number, vector or matrix. Norm[expr, p] gives the p-norm.

Complicated algebraic expressions can usually be written in many different ways. Mathematica provides a variety of functions for converting expressions from one form to ...

Collect[expr, x] collects together terms involving the same powers of objects matching x. Collect[expr, {x_1, x_2, ...}] collects together terms that involve the same powers ...

Decompose[poly, x] decomposes a polynomial, if possible, into a composition of simpler polynomials.

Eliminate[eqns, vars] eliminates variables between a set of simultaneous equations.

With careful attention to branch cuts, Mathematica supports trigonometric functions everywhere in the complex plane, with extensive exact and algebraic transformations, ...

RecurrenceTable[eqns, expr, {n, n_max}] generates a list of values of expr for successive n based on solving the recurrence equations eqns.RecurrenceTable[eqns, expr, nspec] ...

Resolve[expr] attempts to resolve expr into a form that eliminates ForAll and Exists quantifiers. Resolve[expr, dom] works over the domain dom. Common choices of dom are ...

ConstantArray[c, n] generates a list of n copies of the element c.ConstantArray[c, {n_1, n_2, ...}] generates an n_1*n_2*... array of nested lists containing copies of the ...

KarhunenLoeveDecomposition[{a_1, a_2, ...}] gives the Karhunen\[Dash]Loeve transform {b_1, b_2, ...} of the numerical arrays {a_1, a_2, ...} and the transformation matrix m, ...