![covariance matrix matlab covariance matrix matlab](https://i.stack.imgur.com/paNqF.png)
![covariance matrix matlab covariance matrix matlab](https://i.stack.imgur.com/e8h6i.jpg)
Suppose X represents a set of linear regressors. This makes sense because the sum of the squares of the coordinates of a unit-length vector equals one and because the dot product of orthogonal vectors equals zero. Notice that U'*U and V'*V are identity matrices. Subplot(1,3,3) imagesc(S) axis image square colorbar title('S') Subplot(1,3,2) imagesc(V'*V) axis image square colorbar title('V^TV') Subplot(1,3,1) imagesc(U'*U) axis image square colorbar title('U^TU') The columns of U are mutually orthogonal unit-length vectors (these are called the left singular vectors) the columns of V are mutually orthogonal unit-length vectors (these are called the right singular vectors) and S is a matrix with zeros everywhere except for non-negative values along the diagonal (these values are called the singular values). Singular value decomposition (SVD) decomposes a matrix X into three matrices U, S, and V such that: As we will see in later posts, SVD and covariance matrices are central to understanding principal components analysis (PCA), linear regression, and multivariate Gaussian probability distributions.
![covariance matrix matlab covariance matrix matlab](https://1.bp.blogspot.com/_HJ-P1iIFXtk/TSgGhr58vRI/AAAAAAAAAhg/O-cULuv3rDQ/s400/Covariance%2BMatrix%2BCalc%2B02.png)
This post describes singular value decomposition (SVD) and how it applies to covariance matrices.