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In situations where the output's shape changes based on the operation this can be helpful.

    auto accumulate = ...;
    auto a = ...
    auto b = ...
    auto result = a*b;
    for (int row = 0; row < a.rows) {
        accumulate += result[row]
    }
This expression might be entirely valid when a and b are both 2x2 but then becomes incorrect when there's a different shape in b.


Do you mean type instead of shape? I also don't know what you mean by incorrect. C will also create casts when using two different number types in a math operation.


For matrix and quaternions multiplication does not output the same type as the input.

For example:

    int a = 1;
    
    a + a = 2; (int)
    a * 2 = 2; (int)


    auto ma = matrix<2, 4>();
    auto mb = matrix<4, 1>();
 
    ma * a  is matrix<2, 4>
    ma * ma is not possible
    ma * mb is matrix<2, 1>
Compilers used to be very bad at telling you what was going on here if you, for example, changed `<2, 4>` to `<3, 4>` or something. g++ now handles it pretty well: https://hastebin.com/idemopikag


Your original comment was about something being incorrect, now you are talking about error messages, but I don't think either has to do with operator overloading.




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