max and min complex number

i have set that contain complex number, then i get the greatest value using max function and get the smallest value using min function. For example the max value is -0.0115230+0.0474206i and the minimum value is 0.0026796 + 0.0006868i But if i give this command -0.0115230+0.0474206i > 0.0026796 + 0.0006868i it get the result ans=0. So, how did it happen ? should the result is ans=1 ?? please help. i am very confused

Answer 1

[Guillaume]

It can be proven that complex numbers cannot be ordered (under the definition of an ordered field). That means that you cannot compare complex numbers.

As per the documentation, < (and co.) only compare the real part of a number, whereas min returns the complex number with the smallest magnitude.

[ElizabethR]

thanks for answare, Guilaume. But, My problem is i have set of complex number and i want to get the max value and min value from the set of that complex value. So, if there a new complex value, it will be chacked whether it's entered of into the range or not. So, how to make it ?? sorry for my bad english.

[Guillaume]

As I've said there is no ordering on the set of complex numbers. That also means that there is no min and max of complex numbers, since min and max just return the first of last element of the ordered set.

Now you can come up with an ordering function that at first may seem to give an order on the complex number, but it will break under the definition of an ordered field (please read the link).

Mathworks have decided to give a definition to the min and max (maybe the shouldn't have), and as stated that definition compares the magnitudes of the numbers.

Mathworks also have decided to give a definition the comparison operators, but that uses a different ordering than min and max (just compares the real part). The two are not compatible.

Since there's no ordering on the complex numbers, there is also no definition of a range. So within, the field of complex numbers, what you want to do makes no sense, and you should revise your problem.

Consider:

z1 = 5 + 1*1i
z2 = -7 + 3*1i

is

 z3 = 6 + 2*1i

in range? it is if you compare the magnitude, it isn't if you compare the real part, it is if you compare the imaginary part.

[ElizabethR]

thanks for answare Guilaume.. Thanks for your explanation. if you say there is no ordering in complex number, so what should i do ? the set of complex number that i have is represent value of feature extraction of an image. So, if there is new image with new feature extraction, will be chacked whether the result of the feature extraction is in the range of the set of feature extraction or not. so how to make it ? i am really dizzy.

[Guillaume]

Complex numbers are the same as points on a 2D plane. Given a set of points in a plane, can you tell which is the minimum and which is the maximum? No, the concept does not make sense. Same for complex numbers.

Similarly, given a set of points, can you tell if another point is in the range of these points? Well, first you have to define what you mean by the range of a set of points. Until you do that, we can't help you.

Possibly, you can define a point in range of a set of point if it is within the convex hull of the set, but only you can decide that.

[ElizabethR]

yes, thanks for your explanation. Now i am understand about complex number. thank you so much Guillaume.

Answer 2

[Azzi Abdelmalek]

If x1=1.1+2*i and x2=1+2.1*i What is the smallest number ? You can't compare two complex numbers, you can compare their modulus

abs(x1)>abs(x2)

I think max and min function, in your case, are finding the max and min of abs(your_array)

[ElizabethR]

thanks for answare.. ooohh.. why it abs(x1)>abs(2) ?? why not abs(x1)>abs(x2) ??

so, if i have 2 complex number and i want to compare it, it must using absolute ??

[Azzi Abdelmalek]

Obviously, It's abs(x1)>abs(x2). Now it's up to you to tell us how you want to compare x1 and x2, by their modulus, or give us another criterion!

[ElizabethR]

Thanks Azzi. But, i don't know what you mean. My problem is i have set of complex number and i want to get the max value and min value from the set of that complex value. So, if there a new complex value, it will be chacked whether it's entered of into the range or not. So, How to make it ? sorry for my bad english.

[Azzi Abdelmalek]

Ok, to get an answer, you need to clarify one thing:

If x1=1.1+2*i and x2=1+2.1*i What is the smallest value x1 or x2?

[ElizabethR]

thanks for answare Azzi... i don't know. i don't understand about the complex number. So i ask. but, now i understand about the complex number. and the answare for your question is complex number cannot be compared to other complex number so, it can be determined.. it's right ?

you say that complex number can compare from their modulus, whether the modulus is meant is the remainder of the quotient ??

[Stephen23]

@eliz: that is what everyone is telling you. If you wish to create an order then you can use the magnitude.

[ElizabethR]

@stephen, yes.. thank you

[Guillaume]

"If you wish to create an order then you can use the magnitude."

You can, but that ordering is not compatible with addition and multiplication. So, with that ordering, if you have

z1 < z2

You cannot assume that

z1 + c < z2 + c  %c a complex constant
z1 * c < z2 * c, with c > 0 a complex constant

[ElizabethR]

hi Guillaume, thank you so much for your answare and explanation. Yes, now i am understand. Thank you. May i ask once again ? whether you have reference ( ebook ) about complex number ? so i can make strong argument in my task about complex number. God Bless You. sorry for my bad english

Answer 3

[Iain]

Max is calculating the absolute value, and then taking the maximum value, despite being negative.

Greater than is taking the value farthest from negative infinity.

[ElizabethR]

Thanks Lain, but My problem is i have set of complex number and i want to get the max value and min value from the set of that complex value. So, if there a new complex value, it will be chacked whether it's entered of into the range or not. sorry for my bad english.

[Torsten]

Say you have

z1 = 7 + 3*I
z2 = 5 - 6*I

Which number is greater and which number is smaller ?

Best wishes

Torsten.

[Guillaume]

"Max is calculating the absolute value, and then taking the maximum value, despite being negative.Greater than is taking the value farthest from negative infinity."

Neither is true for complex numbers according to the documentation.

[ElizabethR]

@Tortsen, i don't know. i don't understand about the complex number. So i ask. Why you asked back for me ? so how should I answer your question ?

[ElizabethR]

@Guillaume yes thanks.

[Torsten]

@eliz, I asked because your question had already been answered several times and it seemed to me you were not satisfied with these responses. So my guess was that you tried to ask something different, something we did not yet understand.

Best wishes

Torsten.

[ElizabethR]

hi Torsten. oohhh I am Sorry, May be it became misunderstand, it not mean i am not satisfied with the answare, but, i confused so i ask again. But thank you so much. May i ask once again ? whether you have reference ( ebook ) about complex number ? so i can make strong argument in my task about complex number. God Bless You. sorry for my bad english