mldivide

Solving $Ax = B$ for $x$

Usages

x = mldivide(A, B)

x = A \ B

• It solves the system of linear equations $Ax = B$ for $x$.
• A and B should be matrices having the same numbers of rows; otherwise, elementwise division A.\B (or ldivide(A,B)) is performed if any of the following conditions is satisfied:

• If A is a square matrix, LU decomposition is used. It returns an error if A is singular. It reports a warning, and proceeds to compute a solution anyway, if the reciprocal of the condition number of A is less than eps * norm(A), i.e., A nearly singular or badly conditioned.
• If A is not square, QR decomposition is used to obtain a solution that minimises the error $\|Ax - B\|_2$. It reports a warning, and proceeds to compute a solution anyway, if A is rank deficient.