Dot Multiplication in MATLAB

I am a bit confused about how dot multiplication (.*) works in MATLAB. For example, [1 2]' .* [1 2; 3 4] = [1 2; 6 8]. So it seems that each row of the first matrix is being multiplied by the corresponding row in the second matrix. However, [1 2] .* [1 2 3 4]' = [1 2; 2 4; 3 6; 4 8] - it seems that each column of the first matrix is being multiplied by the column vector in the second matrix. Further, [1 2] .* [1 2; 3 4; 5 6]' is not possible because of size incompatibility.

How is the multiplication being carried out? I am using MATLAB R2021b.

Answer 1

[Matt J]

For matrices A and B, the rule is generally that A.* B is element-by-element multiplication a(i,j).*b(i,j), which means that normally all dimensions of A and B must be equal. However if ever size(A,n)=1 and size(B,n)~=1 (or vice versa), then A will be implicitly copied along dimension n until size(A,n)=size(B,n) and similarly for B.

[Matt J]

See also,

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

[Saunok Chakrabarty]

Thanks Matt! This clarifies my doubt. Apologies for the late acceptance.