how to avoid conj

Hello everyone

I have a symbolic vector ,

Xprime=[sin(theta1)*sin(theta2) ,sin(theta1)*cos(theta2) ,cos(theta1)*sin(theta2), cos(theta1)*cos(theta2) ,sin(theta1), cos(theta1) ,sin(theta2) ,cos(theta2)]';

I don't know why Matlab displays:

Xprime =

conj(sin(theta1))*conj(sin(theta2))

conj(cos(theta2))*conj(sin(theta1))

conj(cos(theta1))*conj(sin(theta2))

conj(cos(theta1))*conj(cos(theta2))

conj(sin(theta1))

conj(cos(theta1))

conj(sin(theta2))

conj(cos(theta2))

in the output.

how can I avoid such a problem?

Thank u for answering my question

[Mehran Norouzi]

try this.

a = sym('a','real')

[John D'Errico]

@sanam - Please don't answer your question with a comment. Moved this to a comment:

"and I have used "real" in defining syms"

Answer 1

[John D'Errico]

syms theta theta1 theta2
Xprime=[sin(theta1)*sin(theta2) ,sin(theta1)*cos(theta2) ,cos(theta1)*sin(theta2), cos(theta1)*cos(theta2) ,sin(theta1), cos(theta1) ,sin(theta2) ,cos(theta2)]'

Xprime = 

Did you use a transpose in there? (Yes.) Even though you told MATLAB that the variables are real, they are still called inside functions and operations, where it does not see that the result of those functions is ALWAYS real.

The fact is, the ' operator is a CONJUGATE transpose. So if you don't want a conjugate, then you need to use the .' operator. As you can see here, the conjugate is no longer present.

Xprime=[sin(theta1)*sin(theta2) ,sin(theta1)*cos(theta2) ,cos(theta1)*sin(theta2), cos(theta1)*cos(theta2) ,sin(theta1), cos(theta1) ,sin(theta2) ,cos(theta2)].'

Xprime = 

See the help for transpose, as compared to ctranspose.

help transpose

 .' Transpose.
    X.' is the non-conjugate transpose.
 
    B = TRANSPOSE(A) is called for the syntax A.' when A is an object.
 
    See MATLAB Operators and Special Characters for more details.
 
    See also CTRANSPOSE, PERMUTE, PAGETRANSPOSE.

    Documentation for transpose
       doc transpose

    Other functions named transpose

       categorical/transpose      gpuArray/transpose
       codistributed/transpose    quaternion/transpose
       datetime/transpose         RandStream/transpose
       digraph/transpose          sym/transpose
       dlarray/transpose          tabular/transpose
       duration/transpose

help ctranspose

 '  Complex conjugate transpose.   
    X' is the complex conjugate transpose of X. 
 
    B = CTRANSPOSE(A) is called for the syntax A' (complex conjugate transpose)
    when A is an object.
 
    See MATLAB Operators and Special Characters for more details.
 
    See also TRANSPOSE, PAGECTRANSPOSE.

    Documentation for ctranspose
       doc ctranspose

    Other functions named ctranspose

       categorical/ctranspose      imaqdevice/ctranspose
       codistributed/ctranspose    instrument/ctranspose
       datetime/ctranspose         laurmat/ctranspose
       digraph/ctranspose          quaternion/ctranspose
       dlarray/ctranspose          RandStream/ctranspose
       duration/ctranspose         serial/ctranspose
       gpuArray/ctranspose         sym/ctranspose
       icgroup/ctranspose          tabular/ctranspose
       imaqchild/ctranspose

If you use the conjugate transpose, MATLAB will do what you told it to do, that is, take the conjugate.

[Walter Roberson]

John, you did not tell MATLAB that the symbols are real. If you do then the conj does not appear in the output.

syms theta theta1 theta2 real
Xprime=[sin(theta1)*sin(theta2) ,sin(theta1)*cos(theta2) ,cos(theta1)*sin(theta2), cos(theta1)*cos(theta2) ,sin(theta1), cos(theta1) ,sin(theta2) ,cos(theta2)]'

Xprime = 

"Even though you told MATLAB that the variables are real, they are still called inside functions and operations, where it does not see that the result of those functions is ALWAYS real. "

No, assumptions follow the symbolic variable in the symbolic engine; functions know that the variable is real if they bother to ask the symbolic engine.

syms x real
syms y
is_it_real(x)

ans = logical
   1

is_it_real(y)

Warning: Unable to prove 'imag(y) == 0'.

ans = logical
   0

function tf = is_it_real(SYM)
  tf = isAlways(imag(SYM) == 0);
end