Singular value decomposition

Assignment Help Basic Statistics

Reference no: EM131059928

Using Eq. (3.103a and b) prove the results of Theorem 3.17.

THEOREM 3.17

(Singular Value Decomposition) Let X be a (n x p) data matrix such that p(X) = p ≤n, = 0, and let X^TX and XX^T be (p x p) and (n x n) Grammian matrices respectively, Then

(i) Nonzero latent vectors of XX^T are standardized PCs of X^TX.

(ii) Nonzero latent roots of X^TX and XX^T rare equal.

(iii) Any real (n x p) matrix X can be decomposed as

Reference no: EM131059928

Questions Cloud

Compute correlation loading coefficients : Compute correlation loading coefficients using (a) the correlation matrix, and (b) the covariance matrix. How do the two sets of coefficients compare to each other? Are both sets equally informative? Explain (see also Exercise 3.23).

Spoon absorb from the coffee : A 50.0 g silver spoon at 20.0 °C is placed in a cup of coffee at 90.0 °C. How much heat does the spoon absorb from the coffee to reach a temperature of 89.0 °C?

What is purpose of having a half-wave rectifier in circuit : What is the purpose of having a half-wave rectifier in the circuit? Describe the procedure in this lab to arrive at the final design of both the hardware portion and the software portion to achieve the design objectives?

Red and blue light as it leaves the prism : What is the angle (in degrees) between the red and blue light as it leaves the prism?

Singular value decomposition : (Singular Value Decomposition) Let X be a (n x p) data matrix such that p(X) = p ≤n, = 0, and let XTX and XXT be (p x p) and (n x n) Grammian matrices respectively, Then

Magnitude and direction of the inital velocity : It lands with a velocity of 36m/s at angle of 28 degrees below the horizontal. The positive directions are upward and to the right. Ignoring air resistance, find the magnitude and direction of the inital velocity with which the ball leaves the bat..

Based on an internal rate of return analysis : Quantum Logistics, Inc., a wholesale distributor, is considering the construction of a new warehouse to serve the southeastern geographic region near the Alabama-Georgia border. There are three cities being considered. Based on an internal rate of re..

What is the force between : Two small spheres, 0.200 m from each other are charged. The one on the left has a charge of 0.0001C; the one on the right has a charge of -0.0005C. What is the force between them (magnitude and is it attractive or repulsive)?

What is the future value of this investment : Imagine Homer Simpson actually invested the $200,000 he earned providing Mr. Burns entertainment 7 years ago at 9% annual interest and starts investing an additional $1,700 a year today at the beginning of each year for 15 years at the same 9% annual..

User Account

All Pages