Mathematics

Cholesky, LU, and QR Factorizations

The MATLAB linear equation capabilities are based on three basic matrix factorizations:

• Cholesky factorization for symmetric, positive definite matrices
• LU factorization (Gaussian elimination) for general square matrices
• QR (orthogonal) for rectangular matrices

These three factorizations are available through the chol, lu, and qr functions.

All three of these factorizations make use of triangular matrices where all the elements either above or below the diagonal are zero. Systems of linear equations involving triangular matrices are easily and quickly solved using either forward or back substitution.

Pseudoinverses

Cholesky Factorization