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# slash

(/) right division and feed back

### 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

### History

Version | Description |

5.4.1 | The threshold level for conditioning in slash increased. |

## Comments

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