# Solving a Positive Definite System of Linear Equations (potrs)

potrs solves a system of linear equations $$A X = B$$ with a symmetric positive definite matrix A using the Cholesky factorization computed by potrf.

## Real Variant

The Cholesky factorization reads $$A = U^T U$$ or $$A = L L^T$$.

 A (input/output) real valued SyMatrix The triangular factor $$U$$ or $$L$$ from the Cholesky factorization $$A = U^T U$$ or $$A = L L^T$$, as computed by potrf. B (input/output) real valued GeMatrix On entry, the right hand side matrix $$B$$. On exit, the solution matrix $$X$$.

## Complex Variant

The Cholesky factorization reads $$A = U^H U$$ or $$A = L L^H$$.

 A (input/output) complex valued HeMatrix The triangular factor $$U$$ or $$L$$ from the Cholesky factorization $$A = U^H U$$ or $$A = L L^H$$, as computed by potrf. B (input/output) complex valued GeMatrix On entry, the right hand side matrix $$B$$. On exit, the solution matrix $$X$$.

## Single Right-Hand Side (Real and Complex Variant)

 A (input/output) complex valued HeMatrix The triangular factor $$U$$ or $$L$$ from the Cholesky factorization. b (input/output) complex valued GeMatrix On entry, the right hand side vector $$b$$. On exit, the solution vector $$x$$.