Equal (Built-in Mathematica Symbol)

lhs == rhs returns True if lhs and rhs are identical.

Eigenvalues and Eigenvectors (Mathematica Tutorial)

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 ...

Introduction to Constrained ... (Mathematica Tutorial)

Constrained optimization problems are problems for which a function f(x) is to be minimized or maximized subject to constraints Φ(x). Here f:^n  is called the objective ...

Is the Problem Well-Posed? (Mathematica Tutorial)

DSolve returns a general solution for a problem if no initial or boundary conditions are specified. The general solution to this equation is returned. However, if initial or ...

Advanced Matrix Operations (Mathematica Tutorial)

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 ...

MedianFilter (Built-in Mathematica Symbol)

MedianFilter[image, r] filters image by replacing every value by the median in its range r neighborhood. MedianFilter[data, r] applies median filtering to an array of data.

Minimization and Maximization (Mathematica Tutorial)

Minimization and maximization. Minimize and Maximize yield lists giving the value attained at the minimum or maximum, together with rules specifying where the minimum or ...

Warnings and Messages (Mathematica Tutorial)

Mathematica usually goes about its work silently, giving output only when it has finished doing the calculations you asked for. However, if it looks as if Mathematica is ...

I (Built-in Mathematica Symbol)

I represents the imaginary unit Sqrt[-1].

TreePlot (Built-in Mathematica Symbol)

TreePlot[{v i 1 -> v j 1, v i 2 -> v j 2, ...}] generates a tree plot of the graph in which vertex v_ik is connected to vertex v_jk.TreePlot[{{v i 1 -> v j 1, lbl_1}, ...}] ...