slash

Description

Right division: X=A/B is the solution of X*B=A.

The slash (right division) and backslash (left division) operators are linked by the following equation: B/A=(A'\B')'.

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).

A./B is the element-wise right division, i.e. the matrix with entries A(i,j)/B(i,j). If B is scalar (1x1 matrix) this operation is the same as A./B*ones(A). Same convention if A is a scalar.

Remark that 123./B is interpreted as (123.)/B. In this cases dot is part of the number not of the operator.

System feed back. S = G/.K evaluates S = G*(eye() + K*G)^(-1) this operator avoid simplification problem.

Remark that G/.5 is interpreted as G/(.5). In such cases dot is part of the number, not of the operator.

Comment // comments a line i.e. lines which begin by // are ignored by the interpreter.

Examples

a=[3.,-24.,30.];
B=[
   9.   -36.    30.
  -36.   192.  -180.
   30.  -180.   180.
];
x=a/B
x*B-a // close to zero

a=4 / 2; // Should be 2
a=2 ./ [2,4]; //     1.    0.5
// Comments are good. They help to understand code

See Also

• inv — matrix inverse
• backslash — (\) left matrix division.
• comments — (//) comments

History