linsolve

Solving $Ax = B$ for $x$

Usages

x = linsolve(A, B)

• A and B should be $m\times n$ and $m\times k$, respectively, where $m$ and $k$ are positive integers.
• It solves the system of linear equations $Ax = B$ for $x$.
• 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.
• 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 norm(A)*eps (i.e., A nearly singular or badly conditioned).

[x,r] = linsolve(A, B)

• A and B are matrices as specified for x = linsolve(A,B) above.

• The output x is the same as that obtained by x = linsolve(A,B).

• r is

  • the rank of A when A is not square,
  • the reciprocal of the condition number of A when A is square.

• Warning messages for rank deficiency and badly conditioned matrix are suppressed.