Linear Algebra
Solve linear equations, factor and invert matrices
Blocks
Matrix Factorization
Cholesky Factorization | Factor square Hermitian positive definite matrix into triangular components |
LDL Factorization | Factor square Hermitian positive definite matrices into lower, upper, and diagonal components |
LU Factorization | Factor square matrix into lower and upper triangular components |
QR Factorization | Factor arbitrary matrix into unitary and upper triangular components |
Singular Value Decomposition | Factor matrix using singular value decomposition |
Linear System Solvers
Backward Substitution | Solve UX = B for X when U is upper triangular matrix |
Cholesky Solver | Solve SX = B for X when S is a square Hermitian positive definite matrix |
Forward Substitution | Solve LX = B for X when L is lower triangular matrix |
LDL Solver | Solve SX=B for X when S is square Hermitian positive definite matrix |
Levinson-Durbin | Solve linear system of equations using Levinson-Durbin recursion |
LU Solver | Solve AX = B when A is a square matrix |
QR Solver | Find minimum-norm-residual solution to AX=B |
SVD Solver | Solve AX = B using singular value decomposition |
Matrix Inverses
Cholesky Inverse | Compute inverse of Hermitian positive definite matrix using Cholesky factorization |
LDL Inverse | Compute inverse of Hermitian positive definite matrix using LDL factorization |
LU Inverse | Compute inverse of square matrix using LU factorization |
Pseudoinverse | Compute Moore-Penrose pseudoinverse of matrix |
Topics
- Linear Algebra and Least Squares
Solve systems of linear equations.
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