# NumericComplexEigenPackage Par¶

This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.

characteristicPolynomial: (Matrix Complex Fraction Integer, Symbol) -> Polynomial Complex Fraction Integer

characteristicPolynomial(m, x) returns the characteristic polynomial of the matrix m expressed as polynomial over Complex Rationals with variable x.

characteristicPolynomial: Matrix Complex Fraction Integer -> Polynomial Complex Fraction Integer

characteristicPolynomial(m) returns the characteristic polynomial of the matrix m expressed as polynomial over complex rationals with a new symbol as variable.

complexEigenvalues: (Matrix Complex Fraction Integer, Par) -> List Complex Par

complexEigenvalues(m, eps) computes the eigenvalues of the matrix m to precision eps. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of eps (float or rational).

complexEigenvectors: (Matrix Complex Fraction Integer, Par) -> List Record(outval: Complex Par, outmult: Integer, outvect: List Matrix Complex Par)

complexEigenvectors(m, eps) returns a list of records each one containing a complex eigenvalue, its algebraic multiplicity, and a list of associated eigenvectors. All these results are computed to precision eps and are expressed as complex floats or complex rational numbers depending on the type of eps (float or rational).