FreeMat: RIGHTDIVIDE Matrix Equation Solver/Divide Operator

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RIGHTDIVIDE Matrix Equation Solver/Divide Operator

Section: Mathematical Operators

# Usage

The divide operator `/` is really a combination of three operators, all of which have the same general syntax:

      Y = A / B

where `A` and `B` are arrays of numerical type. The result `Y` depends on which of the following three situations applies to the arguments `A` and `B`:

1. `A` is a scalar, `B` is an arbitrary `n`-dimensional numerical array, in which case the output is the scalar `A` divided into each element of `B`.
2. `B` is a scalar, `A` is an arbitrary `n`-dimensional numerical array, in which case the output is each element of `A` divided by the scalar `B`.
3. `A,B` are matrices with the same number of columns, i.e., `A` is of size `K x M`, and `B` is of size `L x M`, in which case the output is of size `K x L`.

The output follows the standard type promotion rules, although in the first two cases, if `A` and `B` are integers, the output is an integer also, while in the third case if `A` and `B` are integers, the output is of type `double`.

# Internals

There are three formulae for the times operator. For the first form

and the second form

In the third form, the output is defined as:

and is used in the equation `Y B = A`.

# Examples

The right-divide operator is much less frequently used than the left-divide operator, but the concepts are similar. It can be used to find least-squares and minimum norm solutions. It can also be used to solve systems of equations in much the same way. Here's a simple example:

    --> B = [1,1;0,1];
    --> A = [4,5]

    A =
     4 5

    --> A/B

    ans =
     4 1