Some aspects of the array syntax are great, others are a bit puzzling

I have been going through the inroductory material and trying out things as I go. I came across a couple of questions in the arrays section.

First, I tried

[2 4 6 8]*2
   4   8   12   16

Great. Next I tried

[1 2 3;4 5 6]*2
    2   4   6
    8  10  12

Super. If I can multiply an array by a scalar, I wondered if I could multiply a 2 dimensional array by a vector, so I tried

[1 2 3;4 5 6]*[1 2 3]

That got an error indicating that I was confusing matrix multiplication and elementwise multiplication.

So I tried both

[1 2 3 4;2 3 4 5]*[1 2;3 4;5 6;7 8]
   50  60
   66  80
[1 2 3 4;2 3 4 5].*[1 2 3 4]
   1   4   9  16
   2   6  12  20   

This is great,

Then, just to be a pest, I tried:

[1 2 [3 4] 5]
   1  2  3  4  5

What the heck? It seems to me that this should either be an error or the 3rd element should, itself, be a vector.

Finally, I tried

[1 2 3; 4 5 6; 7 8 9'].+[1 2 3]

That got an error. How come I can do element-wise multiplication but not addition?

I have to say that I really like the Alt+Enter to toggle between test and code mode. :-)

Answer 1

[Walter Roberson]

[1 2 [3 4] 5]

is short for

horzcat(1, 2, [3 4], 5)

which in turn would be short for

horzcat(1, 2, horzcat(3, 4), 5)

and there is no problem doing concatenation between a vector and a vector giving a longer vector result.

Consider that you could also have tried

A = [3 4]
[1 2 A 5]

This is valid in MATLAB as long as the number of rows generated by the part to the left of the A in [1 2 A 5] is the same as the number of rows in A, and the number of rows after [1 2 A] is the same as the number of rows in [5]

MATLAB [A B] syntax does not mean to set individual elements with individual scalars A and B: it means to drop in the contents of A and B and concatenate them together on the second dimension (by default), or on the first dimension if you use ; as the delimiter like [1 2;3 4] is vertcat(horzcat(1,2), horzcat(3,4))

How come I can do element-wise multiplication but not addition?

Addition and subtraction and logical and (&) and logical or (|) and relationship operators < and > and == and <= and >= and ~= are always element-by-element already and do not need a special element-by-element form.

[Cynthia Moore]

OK. Back to the tutorial.

[Walter Roberson]

There are only a few operations that have the dot versions:

• .* for element-by-element multiplication instead of algebraic matrix multiplication, also known as inner product
• .^ for element-by-element power instead of matrix power (like repeated matrix multiplication except handles fractional powers too)
• ./ for element-by-element division instead of an operation that is a mix between pinv() and least-squared fitting
• .\ for element-by-element division. This one is undocumented!

[Yair Altman]

Actually, .\ is also fully ducumented, as the ldivide function https://www.mathworks.com/help/matlab/ref/ldivide.html (just as ./ is documented as the rdivide function)

[Walter Roberson]

So it is! I was sure that I had looked before and it wasn't there!