Why can I add a empty array to a scalar variable, but I cannot add an empty array to a vector?

In MATLAB it is possible to add an empty array to a scalar variable, namely,

>> 5 + []

and this results in an empty array. However, adding an empty array to a vector results in a dimension mismatch, namely,

>> [2 3] + []

namely,

Error using + 
Arrays have incompatible sizes for this operation.

Why can I add a empty array to a scalar variable, but I cannot add an empty array to a vector?

Answer 1

[MathWorks Support Team]

This behavior is stated in the documentation and follows the rules of implicit expansion, i.e., dimensions need to match or one of the dimensions must be 1 and the result will have the non-1 result as dimension. The following facts are valid for the aforementioned examples:

>> 5 + [] % 1x1 + 0x0 --> works and result is 0x0, since mismatches have a 1 to compensate.
>> [2 3] + [] % 1x2 + 0x0 --> does not work, since for the 2nd dim, 2 meets 0.

The corresponding documentation page where the implicit expansion is discussed is provided below,

https://www.mathworks.com/help/matlab/matlab_prog/compatible-array-sizes-for-basic-operations.html

The rules of implicit expansion 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.