Module matrix_decomp 

Additional matrix decompositions (QR, Gram–Schmidt) and structure tests. Additional matrix decompositions and structure tests.

Everything here is a method on Matrix (or a free function taking matrices); the module split is purely organisational.

• Decompositions: Matrix::qr (Gram–Schmidt, exact with radicals), Matrix::cholesky, Matrix::ldl, the free function gram_schmidt.
• Structure tests (Option<bool>, None = undecidable): Matrix::is_symmetric, Matrix::is_hermitian, Matrix::is_orthogonal, Matrix::is_unitary, Matrix::is_positive_definite, Matrix::is_positive_semidefinite, Matrix::is_upper_triangular, Matrix::is_lower_triangular, Matrix::is_diagonal, Matrix::is_identity, Matrix::is_zero, Matrix::is_skew_symmetric, Matrix::is_nilpotent.
• Norms: Matrix::norm_1, Matrix::norm_inf, Matrix::norm_p (vectors), plus norm_frobenius in the core module.
• Functions of diagonalizable matrices: Matrix::matrix_pow_symbolic, Matrix::matrix_sqrt, Matrix::matrix_log (any Jordan form with non-zero eigenvalues).
• Calculus: hessian, wronskian, Matrix::casoratian.

Functions

gram_schmidt

Gram–Schmidt orthogonalisation of a list of column vectors.

hessian

Hessian matrix H[i][j] = ∂²f / ∂vars[i] ∂vars[j].

try_wronskian

Wronskian W(f₁, …, fₙ)(x) of a list of functions; see wronskian.

wronskian

Wronskian W(f₁, …, fₙ)(x) = det[ fⱼ^(i) ] of a list of functions.