backslash (\) left matrix division. Syntax X=A\B Description Backslash is the left matrix division: `X=A\B` is a solution to `A*X=B`. If A is square and non-singular `X=A\B` is equivalent to `X=inv(A)*B` in exact arithmetic, but the computations are more accurate and cheaper in floating point arithmetic. Hence, to compute the solution of the linear system of equations `A*X=B`, the backslash operator should be used, and the inv function should be avoided. In the case where A is square, the solution X can be computed either from LU factorization or from a linear least squares solver. If the condition number of A is smaller than `1/(10*%eps)` (i.e. if A is well conditioned), the LU factorization with row pivoting is used. If not (i.e. if A is poorly conditioned), then X is the minimum-norm solution which minimizes ||A*X-B|| using a complete orthogonal factorization of A (i.e. X is the solution of a linear least squares problem). If A is not square, X is a least square solution, i.e. `norm(A*X-B)` is minimal (Euclidean norm). If A is full column rank, the least square solution, `X=A\B`, is uniquely defined (there is a unique X which minimizes `norm(A*X-B)`). If A is not full column rank, then the least square solution is not unique, and `X=A\B`, in general, is not the solution with minimum norm (the minimum norm solution is `X=pinv(A)*B`). `A.\B` is the matrix with (i,j) entry A(i,j)\B(i,j). If A (or B) is a scalar `A.\B` is equivalent to `A*ones(B).\B` (or `A.\(B*ones(A))`. A\.B is an operator with no predefined meaning. It may be used to define a new operator (see overloading) with the same precedence as * or /. Examples See also slash inv pinv percent ieee linsolve umfpack History 5.4.1 The threshold level for conditioning in blackslash increased.