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linsolve

Solving Ax = B for x

x = linsolve(A, B)

  • A should be m×n, and B m×k for any positive integers m and k.
  • It solves the system of linear equations Ax = B for x.
  • If A is not square, QR decomposition is used to obtain a least square solution of Ax = B. 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.