Elementwise Multiplication (Dot Multiplication) of Matrices

I am an instructor of MATLAB at a university. And we traditionally taught that for element-wise multiplication to work, both dimensions (row and column number) of each matrices must be exactly the same. For instance, you could multiply a 1x3 array with another 1x3 array, but not with a 4x1 array. And it used to be like that, otherwise, it would give an error, saying "matrix dimensions must agree".

I just noticed that at least in MATLAB 2017a, you actually can multiply various sizes of arrays element-wise. For example, you can multiply a 1x3 array with a 4x1 array, getting a 3x4 array. However, you still cannot element-wise multiply a 1x3 array with a say, 2x2 array. What is the rule for the dimensions when doing elemnent-wise multiplication there? And in which edition of MATLAB this change occurred?

Thank you.

Answer 1

[Star Strider]

It’s called ‘implicit expansion’, and was introduced in R2016b.

I can’t find a specific link to it. You can find it under Mathematics in the Release Notes (link) for R2016b.

[Chuck]

Thank you so much! So this applies only to vectors (one dimension being 1) and matrices of compatible sizes...

[James Tursa]

It applies to any two arrays as long as there is not a mismatch in an index where both dimensions are not equal to 1 and also not equal to each other. So not just for vectors and matrices.

[Star Strider]

As always, my pleasure!