The singular value decomposition theorem

Assignment Help Basic Statistics

Reference no: EM131059855

Let X⁺=P?⁺_(r)^Tbe the generalized inverse of a (n x p) matrix X (Theorem 5.1). Show that the following relations hold:

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

Reference no: EM131059855

Questions Cloud

Same direction at the same speed : What force is needed so that a 100 Kg box moving on a frictionless floor on a straight line at the speed of 1 m/s keeps moving for another 100 minutes in the same direction at the same speed?

Discuss the rationale behind risk-based capital requirements : Discuss the rationale behind risk-based capital requirements.

Current total value-what is the debt-equity ratio : Neal Enterprises has no debt. Its current total value is $75.2 million. Assume the company sells $34.6 million in debt. Requirement 1: Ignoring taxes, what is the debt-equity ratio? (Do not round intermediate calculations. Round your answer to 2 deci..

Identify consumers who are most likely to buy your product : Identify the consumers who are most likely to buy your product in terms of: (a) their demographic characteristics and (b) any other kind of characteristics you believe are important.

The singular value decomposition theorem : 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:

Problem regarding the acceleration of the bicycle : A boy on a bicycle increases his velocity from 5 m/s to 20 m/s in 10 seconds. a) What is the acceleration of the bicycle?

How improving health in that modality will improve health : In the lecture you saw that there are four holistic modalities to self-physical, mental, emotional, and spiritual. Choose one modality and discuss how improving health in that modality will improve health in the whole being. Give examples from you..

What is its required return : Suppose Paccar’s current stock price is $84.36 and it is likely to pay a $3.94 dividend next year. Since analysts estimate Paccar will have an 4.2 percent growth rate, what is its required return?

What is the acceleration of the car : A car accelerates uniformly from 0 to 72 km/h in 11.5 seconds. a) What is the acceleration of the car in m/s2?

User Account

All Pages