Rank complement of diagonalizable matrices using polynomial functions

摘要: This report defines the rank complement of a diagonalizable matrix (i.e. which can be brought to diagonal form by means change basis) as interchange range and null space. Given A there is in general no unique Ac has equal space A, only matrices full have complement; zero matrix. Consequently, operation not distinct operation, but rather characterization any makes an One particular introduced here, eventually leads implementation operations terms polynomials A. The main result that for each possible r polynomial evaluates provides explicit expressions compute symmetric These results are then generalized case matrices. Finally, Matlab function described implements based on derived.