How to get a scalar from MATLAB

If I have two matrices w is A 1*50 matrix and B is a 1*50 matrix. I want to use this formula of rp= w'r to calculate the result. This is the original formula to calculate the portfolio return. In this formula, w is an n*1 matrix and r is also an n*1 matrix. So, w' is a 1*n matrix. Thus we can get a scalar. But if I want to replace w' with A and replace r with B and I want to get a scalar in MATLAB. But I wrote codes below, it turn into a 50*50 matrix.

I want to know why this happen and how can I switch the matrix into a scalar.

A=[1:50];
B=[1:50];
rp1=A .* B.';

And if I use rp=A.*B. It will becomes a 1*50 matrix. Can I sum this matrix to get the scalar? (But it cannot make sence write?)

Thanks in advance!

A=[1:50];
B=[1:50];
rp2=A .* B.;
sum(rp2);

[Stephen23]

"But it cannot make sence write?"

Matrix multiplication does make sense, therefore you can use MTIMES:

A = 1:50; % removed the superfluous square brackets
B = 1:50; % removed the superfluous square brackets
A * B.'

ans = 42925

https://www.mathworks.com/help/matlab/ref/double.transpose.html

https://www.mathworks.com/help/matlab/ref/double.mtimes.html

"I want to know why this happen..."

You used TIMES, which is the wrong operation:

https://www.mathworks.com/help/matlab/ref/double.times.html

https://www.mathworks.com/help/matlab/matlab_prog/array-vs-matrix-operations.html

[Amy]

I've tried that but cannot work. It's strange, but thanks!

Answer 1

[Star Strider]

Probably the easiest way to do what you want is to use the dot function —

A=[1:50];
B=[1:50];
rp = dot(A,B)

rp = 42925

It doesn’t care whether one may be a row vector and the other a column vector.

.

[Amy]

It works. Thanks!

[Star Strider]

As always, my pleasure!

[dpb]

A=[1:50]; B=A;
dot(A,B)

ans = 42925

sum(A.*B)

ans = 42925

A*B'

ans = 42925

All ":work" if both A, B are row vectors for a slightly different interpretation of what the expressions mean.

As noted in earlier Answer, In order for the mathematics of the original paper to be correct, rp= w'r, then both r and w have to be column vectors.To follow the paper's convention you would instead have written

A=[1:50].'; B=A;   % create A, B to mimic w, r from paper
A.'*B

ans = 42925

Alternatively, one can use MATLAB syntax convention even if for some other reason were to stick with row vectors by use of the colon expansion rule--

A=[1:50]; B=A;  % both row vectors
A(:)'*B(:)      % return as columns

ans = 42925

Answer 2

[dpb]

A=[1:50];
B=[1:50];
rp1=A*B'

rp1 = 42925

Matrix multiplication is defined such that the resultant matrix is the size of the outer dimensions while the inner dimensions must be conforming , thus

[1xN].' * [1xN] --> [Nx1] * [1xN] --> [NxN]

whereas

[1xN] * [1xN].' --> [1xN] * [Nx1] --> [1x1]

In MATLAB the "dot" operator, .* is element-wise multiplication of conforming arrays or matrices.

In the original, to produce a single element, the w vector would have to have been a column vector, not a row vector, in which case the [Nx1]' operation would create the needed [1xN].

ERRATUM: Actually, both w and r must be column vectors for the original math to be correct...amplified in a comment above...