# Compatible Array Sizes for Basic Operations

Most binary (two-input) operators and functions in MathJSLab support numeric
arrays that have compatible sizes. Two inputs have compatible sizes if, for
every dimension, the dimension sizes of the inputs are either the same or one
of them is 1. In the simplest cases, two array sizes are compatible if they are
exactly the same or if one is a scalar. MathJSLab implicitly expands arrays
with compatible sizes to be the same size during the execution of the
element-wise operation or function.

## Inputs with Compatible Sizes

### 2-D Inputs

These are some combinations of scalars, vectors, and matrices that have
compatible sizes:

- Two inputs which are exactly the same size.
- One input is a scalar.
- One input is a matrix, and the other is a column vector with the same number
  of rows.
- One input is a column vector, and the other is a row vector.

### Multidimensional Arrays

Every array in MATLAB has trailing dimensions of size 1. For multidimensional
arrays, this means that a 3-by-4 matrix is the same as a matrix of size
3-by-4-by-1-by-1-by-1. Examples of multidimensional arrays with compatible
sizes are:

- One input is a matrix, and the other is a 3-D array with the same number of
  rows and columns.
- One input is a matrix, and the other is a 3-D array. The dimensions are all
  either the same or one of them is 1.

### Empty Arrays

The rules are the same for empty arrays or arrays that have a dimension size of
zero. The size of the dimension that is not equal to 1 determines the size of
the output. This means that dimensions with a size of zero must be paired with
a dimension of size 1 or 0 in the other array, and that the output has a
dimension size of 0.

> > `A: 1-by-0` `B: 3-by-1` `Result: 3-by-0`

## Inputs with Incompatible Sizes

Incompatible inputs have sizes that cannot be implicitly expanded to be the
same size. For example:

- One of the dimension sizes are not equal, and neither is 1.
    > `A: 3-by-2` `B: 4-by-2`
- Two nonscalar row vectors with lengths that are not the same.
    > `A: 1-by-3` `B: 1-by-4`