Question

I was just curious why Matlab can compare an empty matrix to a singleton matrix. In particular

>> [] == [1]

ans =

[]

It just seems odd that it would do that and I’m just wondering why it would do that. This also works for other comparison operations (<=, <, >=, >, !=). It gives an error if the size of the row or column is greater than one.

Thanks!

Edit: I also believe they do this for other operators, such as addition, subtraction, etc.

Answer 1

[] (empty matrix) is considered a valid matrix representation of size 0x0 by MATLAB. From the documentation for the eq function, which is what gets called when you use operator == to compare matrices, the behavior is as follows:

A == B compares each element of array A for equality with the
corresponding element of array B, and returns an array with elements
set to logical 1 (true) where A and B are equal, or logical 0 (false)
where they are not equal. Each input of the expression can be an array
or a scalar value.

…

If one input is scalar and the other a nonscalar array, then the
scalar input is treated as if it were an array having the same
dimensions as the nonscalar input array.

In the comparison [] == [1], the left operand is non-scalar (isscalar([]) returns 0) while the right operand is scalar. So scalar expansion rules apply, and the scalar operand is expanded to the dimensions of the non-scalar operand (in this case 0x0), and the result is an empty matrix.