The problem is that the covariance matrix becomes very large here. Luckily, it's not necessary to compute this matrix explicitly: It's enough to compute a matrix xc such that C = xc' * xc. Then, instead of computing eig(C) it's equivalent to compute svd(xc). I explain a bit more in the code below:
mslpJune_dt_reshaped = randn(1440*81, 43);
mslpJune_dt_reshaped_trans = transpose(mslpJune_dt_reshaped);
% COV would return a matrix that's too large to store. Let's take the lines
% of code that COV does internally (see "edit cov") and see where that gets us:
x = mslpJune_dt_reshaped_trans;
[m,n] = size(x);
denom = m - 1;
xc = x - sum(x,1)./m; % Remove mean
%c = (xc' * xc) ./ denom; % Still can't afford this last one
xc = xc ./ sqrt(denom); % now, C = xc' * xc
% Compute the SVD of xc:
[U, S, V] = svd(xc, 'econ'); % Could also use svds(xc, 2) to get only the two largest singular values
% We know that xc = U*S*V', therefore C = xc'*xc = V*S*U'*U*S*V'
% and because U is orthogonal, U'*U cancels out and we have
% C = V*S*S*V', and therefore we can treat V as the matrix of eigenvectors
% and the square of the singular values on the diagonal of S as the
% eigenvalues:
eigenvectors = V;
eigenvalues = S*S;
% Verify these are really the eigenvalues and eigenvectors of C = xc'*xc:
norm(xc'*(xc*eigenvectors) - eigenvectors*eigenvalues)
