Question

Use the svd() function in MATLAB to compute , the rank-1 approximation of . Clearly state what is, rounded to 4 decimal places. Also, compute the root mean square error (RMSE) between and .

Answer 1

Answer:

Here is the Matlab code.

Step-by-step explanation:

Matlab Code:

$A = [1 2 2;3 4 5;6 7 8]\\[U,S,V] = svd(A)u1 = U(:,1)\\u2 = U(:,2)\\u3 = U(:,3)\\d1 = dot(u1,u2)\\c = cross(u1,u2)\\d2 = dot(c,u3)$

$d1 =- 5.5511e-17\\c = -0.7172 0.6643 -0.2103\\d2 = 1$  

Yes, since c = cross(u1,u2) is orthogonal to both u1 and u2. Hence is u3, thus the dot product with u3 is 1.