Transposing matrix using reshape
What is the difference between .' and ' when transposing a matrix?
Difference between .' and ' for taking the transpose of a matrix?
Transpose a vector under certain conditions
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I don't think this is discussed anywhere here: https://www.mathworks.com/help/matlab/ref/transpose.html
It just says .' is the notation, even though ' has been working just fine for me.
It has a note about ' in the context of imaginary numbers, but I'm wondering about using this operator on matrices. Are .' and ' completely equivalent for matrices?
I know the . prefix usually makes an operation elementwise, but I'm not sure what that would mean in the context of taking a transpose
Interesting question!
I would definitely say it's good practice to use .' when you just want to transpose, even if the numbers are real and thus ' would have the same effect. The mains reasons for this are:
Conceptual clarity: if you need to transpose, just transpose. Don't throw in an unnecessary conjugation. It's bad practice. You'll get used to writing
'to transpose and will fail to notice the difference. One day you will write'when.'should be used. As probable illustrations of this, see this question or this one.Future-proofness. If one day in the future you apply your function to complex inputs the behaviour will suddenly change, and you will have a hard time finding the cause. Believe me, I know what I say1.
Of course, if you are using real inputs but a conjugation would make sense for complex inputs, do use '. For example, if you are defining a dot product for real vectors, it may be appropriate to use ', because should you want to use complex inputs in the future, the conjugate transpose would make more sense.
1 In my early Matlab days, it took me quite a while to trace back a certain problem in my code, which turned out to be caused by using ' when I should have used .'. What really got me upset is, it was my professor who had actually said that ' meant transpose! He forgot to mention the conjugate, and hence my error. Lessons I learned: ' is not .'; and professors can tell you things that are plain wrong :-)
My very biased view: Most cases I use ' are purely "formal", aka not related to mathematical calculations. Most likely I want to rotate a vector like the index sequence 1:10 by 90 degrees.
I seldomly use ' to matrices since it's ambiguous - the first question you've to answer is why you want to make a transpose?
If the matrix is originally defined in a wrong direction, I would rather define the matrix in the correct one it should be, but not turning it afterwards.
To transpose a matrix for a mathematical calculation, I explicitly use transpose and ctranspose. Because by doing so the code is easier to read (don't have to focus on those tiny dots) and to debug (don't have to care about missing dots). Do the following jobs such as dot product as usual.