# ldivide, .\

Left array division

## Syntax

``x = B.\A``
``x = ldivide(B,A)``

## Description

example

````x = B.\A` divides each element of `A` by the corresponding element of `B`. The sizes of `A` and `B` must be the same or be compatible.If the sizes of `A` and `B` are compatible, then the two arrays implicitly expand to match each other. For example, if one of `A` or `B` is a scalar, then the scalar is combined with each element of the other array. Also, vectors with different orientations (one row vector and one column vector) implicitly expand to form a matrix.```
````x = ldivide(B,A)` is an alternative way to divide `A` by `B`, but is rarely used. It enables operator overloading for classes. ```

## Examples

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Create two numeric arrays, `A` and `B`, and divide the second array, `B`, into the first, `A`.

```A = ones(2,3); B = [1 2 3; 4 5 6]; x = B.\A```
```x = 2×3 1.0000 0.5000 0.3333 0.2500 0.2000 0.1667 ```

Create a scalar, `c`, and divide it by a numeric array. The result is the same size as the array.

```c = 2; D = [1 2 3; 4 5 6]; x = D.\c```
```x = 2×3 2.0000 1.0000 0.6667 0.5000 0.4000 0.3333 ```

Create a 1-by-2 row vector and 3-by-1 column vector and divide them.

```a = 1:2; b = (1:3)'; b .\ a```
```ans = 3×2 1.0000 2.0000 0.5000 1.0000 0.3333 0.6667 ```

The result is a 3-by-2 matrix, where each (i,j) element in the matrix is equal to `b(i) .\ a(j)`:

`$\mathit{a}=\left[{\mathit{a}}_{1}\text{\hspace{0.17em}}{\mathit{a}}_{2}\right],\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathit{b}=\left[\begin{array}{c}{\mathit{b}}_{1}\\ {\mathit{b}}_{2}\\ {\mathit{b}}_{3}\end{array}\right],\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\text{\hspace{0.17em}}\mathit{b}\text{\hspace{0.17em}}.\\text{\hspace{0.17em}}\mathit{a}=\left[\begin{array}{cc}{\mathit{b}}_{1}\text{\hspace{0.17em}}.\\text{\hspace{0.17em}}{\mathit{a}}_{1}& {\mathit{b}}_{1}\text{\hspace{0.17em}}.\\text{\hspace{0.17em}}{\mathit{a}}_{2}\\ {\mathit{b}}_{2}\text{\hspace{0.17em}}.\\text{\hspace{0.17em}}{\mathit{a}}_{1}& {\mathit{b}}_{2}\text{\hspace{0.17em}}.\\text{\hspace{0.17em}}{\mathit{a}}_{2}\\ {\mathit{b}}_{3}\text{\hspace{0.17em}}.\\text{\hspace{0.17em}}{\mathit{a}}_{1}& {\mathit{b}}_{3}\text{\hspace{0.17em}}.\\text{\hspace{0.17em}}{\mathit{a}}_{2}\end{array}\right].$`

Since R2023a

Create two tables and divide the second table into the first. The row names (if present in both) and variable names must be the same, but do not need to be in the same orders. Rows and variables of the output are in the same orders as the first input.

`B = table([1;2],[3;4],VariableNames=["V1","V2"],RowNames=["R1","R2"])`
```B=2×2 table V1 V2 __ __ R1 1 3 R2 2 4 ```
`A = table([4;2],[3;1],VariableNames=["V2","V1"],RowNames=["R2","R1"])`
```A=2×2 table V2 V1 __ __ R2 4 3 R1 2 1 ```
`x = B .\ A`
```x=2×2 table V1 V2 ___ _______ R1 1 0.66667 R2 1.5 1 ```

## Input Arguments

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Operands, specified as scalars, vectors, matrices, multidimensional arrays, tables, or timetables. Inputs `A` and `B` must either be the same size or have sizes that are compatible (for example, `A` is an `M`-by-`N` matrix and `B` is a scalar or `1`-by-`N` row vector). For more information, see Compatible Array Sizes for Basic Operations.

• If `A` or `B` is an integer data type, then the other input must be the same integer type or be a scalar double. Operands with an integer data type cannot be complex.

Inputs that are tables or timetables must meet the following conditions: (since R2023a)

• If an input is a table or timetable, then all its variables must have data types that support the operation.

• If only one input is a table or timetable, then the other input must be a numeric or logical array.

• If both inputs are tables or timetables, then:

• Both inputs must have the same size, or one of them must be a one-row table.

• Both inputs must have variables with the same names. However, the variables in each input can be in a different order.

• If both inputs are tables and they both have row names, then their row names must be the same. However, the row names in each input can be in a different order.

• If both inputs are timetables, then their row times must be the same. However, the row times in each input can be in a different order.

Data Types: `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64` | `logical` | `duration` | `char` | `table` | `timetable`
Complex Number Support: Yes

## Tips

• The element-wise operators `./` and `.\` are related to each other by the equation `A./B = B.\A`.

• When dividing integers, use `idivide` for more rounding options.

• MATLAB® does not support complex integer division.

## Version History

Introduced before R2006a

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