why the coefficient of case 2 is 2 columns, not 5 columns? (about coefficient value of PCA)

(1) Case 1

[coeff] = pca(rand(5,3))

coeff = 3×3

0.7120 -0.5694 -0.4109 0.6460 0.3020 0.7010 0.2750 0.7646 -0.5829

(2) Case 2

[coeff] = pca(rand(5,3)')

coeff = 5×2

-0.0054 0.1255 -0.4611 0.2098 -0.1677 0.8905 -0.5702 -0.3811 0.6588 0.0448

why the coefficient of case 2 is 2 columns, not 5 columns?

Answer 1

[Jon]

By default pca gives the 'economy' option which only includes significant components. for pca(X) with X n by p using 'economy' false will give a p by p coefficient matrix as you expected

 [coeff] = pca(rand(5,3)','economy',false)

coeff =

   -0.4049   -0.1882    0.5939   -0.5462    0.3867
   -0.5332    0.5469   -0.2904    0.2565    0.5162
    0.3748    0.7458    0.5429   -0.0101   -0.0925
   -0.1896   -0.2715    0.5169    0.7893   -0.0096
    0.6126   -0.1887   -0.0324    0.1128    0.7585

[HYUN SEOK]

Thanks a lot