Documentation

# ldivide, .\

Left array division

## 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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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

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):

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

## Input Arguments

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Operands, specified as scalars, vectors, matrices, or multidimensional arrays. Numeric 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.

• If A and B are duration arrays, then they must be the same size unless one is a scalar.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical | duration | char
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.

## Compatibility Considerations

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Behavior changed in R2016b