Abstract: By using the theory of matrix factorization and generalized inverse, we gave the calculation formulas of the polar factorization and generalized inverse for universal extended matrix, and deduced  some perturbation bounds for the polar factorization of universal extended matrix. The results show that the method not only keeps the numerical accuracy, but also reduces the calculation amount and storage capacity.

Key words: universal extended matrix, polar factorization, generalized inverse, perturbation bound