Let X+=P?+(r)T be the generalized inverse of a (n x p) matrix X (Theorem 5.1). Show that the following relations hold:
![](https://test.transtutors.com/qimg/7ac6e3db-ff4d-4682-84bc-c36ee14a232f.png)
THEOREM 5.1
(The Singular Value Decomposition Theorem) Let X be a (n x p) data matrix of reduced rank rpthen there exists a real (n × r) matrix Q, a real ( p × r ) matrix P, and a real (r × r) diagonal matrix
?(r) such that
![](https://test.transtutors.com/qimg/d6775558-5752-4e2d-9cef-4007ce4cdb89.png)
![](https://test.transtutors.com/qimg/aee8fe29-ac20-42ae-90cc-479257352635.png)