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When transposing vectors/matrices in MATLAB, I've seen and used just the ' (apostropohe) operator for a long time.

For example:

>> v = [ 1 2 3 ]'

v = 

    1
    2
    3

However this is the conjugate transpose as I've recently found out, or ctranspose.

This seems to only matter when there are complex numbers involved, where if you want to transpose a matrix without getting the conjugate, you need to use the .' opertator.

Is it good practice to also use the .' for real matrices and vectors then? What should we be teaching MATLAB beginners?

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    Hi @rayryeng, thank you! I saw your replies to a few Matlab posts recently! I'm in awe. I've been lurking around, finally have a bit of courage to start contributing. Great dialogue between you, Luis Mendo, and Yvon. Commented Aug 6, 2014 at 0:42
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    @legas It's a good idea to contribute. You'll find you learn a lot by answering and seeing other people's answers. My Matlab skills have improved a lot that way. But watch out, it can be very addictive :-) Commented Aug 6, 2014 at 1:16
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    @LuisMendo - I definitely agree. I've had a SO account for 6 months, but I didn't start actively answering questions until about 3 months ago. Over 3 months, I gained about 6500 reputation.... answering questions is very addictive! Commented Aug 6, 2014 at 1:20
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    +1 nice question. It's a good practice distinguishing between ' and .' even when you have nothing to do with complex numbers. Much like avoiding the use of i and j as variable names. Commented Aug 6, 2014 at 5:57
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    One thing just forgot to mention. I'm really confused by the . Try to follow the pattern - "The . in A.*B means to perform * on each element in A and B; the . in A./B means to perform / on each element in A and B; the .' in A.' means to perform ' on ??? in A ?? How much sense does it make that "element-wise transpose" a matrix? If I were the student how could I establish an analogy between .* and .'? Commented Aug 6, 2014 at 8:20

4 Answers 4

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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:

  1. 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.

  2. 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 :-)

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10 Comments

Hahahah! I made a reference to you in my post... and look who decides to write one :) +1 from me
@rayryeng I couldn't resist answering. You know what strong feelings I have on this :-)
Thanks you, yes I was also taught ' and the exact same problem happened to me, took me SO LONG to find it. :)
@legas - I remember the first time I encountered this slight (but disastrous) difference. I was implementing the DFT on my own without using any built-in functions. To do this vectorized, this requires you to compute a matrix of complex coefficients. To do the inverse, you simply have to transpose the matrix. It took me several hours to figure out why it wasn't working... and that's because I used ' instead of .'... d'oh! Like Luis, it's an experience like this that ingrains the concept of ' and .' to be forever stuck in your head.
I'm still fairly new to Stack Overflow etiquette, can I accept everyone's answer? Otherwise I choose this one because @LuisMendo has "Matlab's ' is not transpose; .' is." in his profile blurb haha!
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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.

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6 Comments

Very nicely put. I agree with the non-ambiguity. +1
I mostly agree with you here except that I have found that sometimes you will define a matrix correctly, use a built-in function on it, and the built-in function will have mysteriously transposed it. I have started peppering my code with statements such as vectorOut = reshape(vectorOut,size(vectorIn)); to enforce a consistent matrix shape.
@rayryeng I also learned ambiguity and avoiding it in a hard way. But luckily it took me not so long to learn to be prudent when naming variables and choosing functions (before actually keyboarding the code!).
@legas Will it help if you add an example with complex numbers?
@Yvon - Whenever I give MATLAB seminars, this is one of the points I always stress, so yes an example is always good. A bonus is to show them that using ' to compute the magnitude squared of a complex vector.
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This is actually a subject of debate among many MATLAB programmers. Some say that if you know what you're doing, then you can go ahead and use ' if you know that your data is purely real, and to use .' if your data is complex. However, some people (such as Luis Mendo) advocate the fact that you should definitely use .' all the time so that you don't get confused.

This allows for the proper handling of input into functions in case the data that are expected for your inputs into these functions do turn out to be complex. There is a time when complex transposition is required, such as compute the magnitude squared of a complex vector. In fact, Loren Shure in one of her MATLAB digests (I can't remember which one...) stated that this is one of the reasons why the complex transpose was introduced.

My suggestion is that you should use .' always if your goal is to transpose data. If you want to do some complex arithmetic, then use ' and .' depending on what operation / computation you're doing. Obviously, Luis Mendo's good practices have rubbed off on me.

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1 Comment

It might be too detailed for a beginner to distinguish ' and .' for his/her first day with Matlab. But once introduced with a real problem, it should be the teacher's duty to stress the student on the differences (poor Luis :(
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There are two cases to distinguish here:

  1. Taking transpose for non-mathematical reasons, like you have a function that is treating the data as arrays, rather than mathematical vectors, and you need your error correcting input to get it in the format that you expect.
  2. Taking transpose as a mathematical operation.

In the latter case, the situation has to dictate which is correct, and probably only one of the two choice is correct in that situation. Most often that will be to take the conjugate transpose, which corresponds to ', but there are cases where you must take the straight transpose and then, of course, you need to use .'.

In the former case, I suggest not using either transpose operator. Instead you should either use reshape or just insist that the input be make correctly and throw an error if it is not. This clearly distinguishes these "computer science" instance from true mathematical instances.

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1 Comment

For an arbitrary matrix, I don't think you can achieve transpose behaviour with reshape (you can for vectors)

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