LyapunovSolve (Built-in Mathematica Symbol)

LyapunovSolve[a, c] finds a solution x of the matrix Lyapunov equation a.x + x.a\[ConjugateTranspose] == c.LyapunovSolve[a, b, c] solves a.x + x.b == c.LyapunovSolve[{a, d}, ...

SeedRandom (Built-in Mathematica Symbol)

SeedRandom[n] resets the pseudorandom generator, using n as a seed. SeedRandom[] resets the generator, using as a seed the time of day and certain attributes of the current ...

HilbertMatrix (Built-in Mathematica Symbol)

HilbertMatrix[n] gives the n*n Hilbert matrix with elements of the form 1/(i + j - 1).HilbertMatrix[{m, n}] gives the m*n Hilbert matrix.

Stiffness Detection (Mathematica Tutorial)

Many differential equations exhibit some form of stiffness, which restricts the step size and hence effectiveness of explicit solution methods. A number of implicit methods ...

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 ...

$MinPrecision (Built-in Mathematica Symbol)

$MinPrecision gives the minimum number of digits of precision to be allowed in arbitrary-precision numbers.

Det (Built-in Mathematica Symbol)

Det[m] gives the determinant of the square matrix m.

NullSpace (Built-in Mathematica Symbol)

NullSpace[m] gives a list of vectors that forms a basis for the null space of the matrix m.

HermitianMatrixQ (Built-in Mathematica Symbol)

HermitianMatrixQ[m] tests whether m is a Hermitian matrix.

SymmetricMatrixQ (Built-in Mathematica Symbol)

SymmetricMatrixQ[m] tests whether m is a symmetric matrix.