PCA output of Matlab's pca() function doesn't match manual calculation

Question

I try to calculate the PCA in my matrix and I use two ways for this:

1. PCA function

   [coeff, score, eigenvalues] = pca(M);
   

2. And for compare and understand the PCA calculus, I try to calculate step by step the PCA without the matlab function pca.

   %// first I "z-scored" my matrix
   X = zscore(M);
   %// second I calculate the covariance matrix
   %// this matrix is equals to the correlation matrix
   V = cov(X);
   %// Third, I calculate the eigenvalues(E) and eigenvectors(U)
   [U,E] = eig(V);
   

The pca function's eigenvalues are not equal to E and I think the columns of U are principal components and rows of U are variables and it's not equal to coeff.

So, I think that I don't understand how calculate the PCA of a matrix?

Answer 1

The problem is the zscore function. If I do a "manual" z-scoring in my matrix I find the same result as with pca:

M = [10,5,14;12,5,45;123,58,42];
%// "manual" zscore
stdr = std(M);
X = M./repmat(stdr,size(M,1),1);
%// "manual" PCA
V = cov(X);
[U,E] = eig(V);
%// with pca function
[coeff,score,eigenvalue] = pca(X);

E equals eigenvalue and coeff equals U so I'm ok, I think I understand how calculate a PCA.