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# slash

(/) right divisions. System's feed back. Comments

### Syntax

X = A / B // while A = X * B X = A ./ B // while A = X .* B X = A ./. B // while A = X .*. B S = G /. K // on-row comment /* block of multilines comments */

### 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.

System feed back. `S = G/.K`

evaluates
`S = G*(eye() + K*G)^(-1)`

this operator avoid
simplification problem.

Note that `123./B` is interpreted as `(123)./B` .
In this case, the dot is part of the operator, not of the decimal number.
In the opposite, `G/.5` is interpreted as `G/(.5)` :
The dot here is part of the number, while it is not the case in
`G/. 5` |

Comment `//`

comments a line i.e. lines which begin by
`//`

are ignored by the interpreter.

It is the same with `/*`

which start to comment a block of code
and with `*/`

which end to comment this block.

### 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]

Kronecker right division :

A = [1 100 ; 10 1000], B = [1 2 4], P = A .*. B P ./. B

--> A = [1 100 ; 10 1000], B = [1 2 4], A = 1. 100. 10. 1000. B = 1. 2. 4. --> P = A .*. B P = 1. 2. 4. 100. 200. 400. 10. 20. 40. 1000. 2000. 4000. --> P ./. B ans = 1. 100. 10. 1000.

// Comments are good. They help to understand code a = 1; // Comment after some heading instructions /* Even long, that is to say on many lines, comments are useful */

### See also

- inv — matrix inverse
- backslash — (\) left matrix division: Exact or least square solution
- kron ./. — Kronecker left and right divisions
- comments — (// or /*...*/) comments
- overloading — display, functions and operators overloading capabilities

### History

Version | Description |

5.4.1 | The threshold level which switches between Gaussian Elimination with row pivoting and linear least squares when computing B/A is decreased from sqrt(eps) to eps. |

6.0.0 | 1./B means now 1 ./ B, no longer 1. / B |

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