Givens transformation and QR factorization of complex matrix
There is a mature algorithm of the triangle factorization of the real matrix,but there is not a good one of that of the complex matrix.To solve the problem on the triangle factorization of the complex matrix,This paper uses the scientific analogy,redefinition,extending the definition,and deduction to solve this problem.It gives a definition for the complex Givens matrix.It also deduces that the complex Givens matrix is a Unitary matrix.It gets the algorithm of rotating a complex vector to any fixed direction by finite complex Givens transformations.It proves that any nonsingular complex matrix can be factorized in a product between a Unitary matrix and a complex nonsingular upper triangular matrix by finite complex Givens transformations.It solves the QR factorization of the complex matrix by the complex Givens transformations.