Question on a linear algebra problem.

(a) With A = [{1, i, 0}, {i, 0, 1}], use elimination to solve Ax = 0

(b) Show that the nullspace you just computed is orthogonal to C(A^H) and not to the usual row space C(A^T). The four fundamental spaces in the complex case are N(A) and C(A) as before, and then N(AH) and C(A^H).

The nullspace I got in part a) is orthogonal to C(A^T), not C(A^H). it is {i,-1,1}.

Did I get the right nullspace? If so or If not, what have I done wrong?

Any help will be greatly appreciated. Thank you.

Question

Question on a linear algebra problem.

(a) With A = [{1, i, 0}, {i, 0, 1}], use elimination to solve Ax = 0

(b) Show that the nullspace you just computed is orthogonal to C(A^H) and not to the usual row space C(A^T). The four fundamental spaces in the complex case are N(A) and C(A) as before, and then N(AH) and C(A^H).

The nullspace I got in part a) is orthogonal to C(A^T), not C(A^H). it is {i,-1,1}. 

Did I get the right nullspace? If so or If not, what have I done wrong? 

Any help will be greatly appreciated. Thank you.

anonymous · Answer

@ikram002p  I don't understand the problem, please, help

anonymous · Answer

@dan815

dan815 · Answer

@abb0t

abb0t · Answer

Welcome to OpenStudy, @JKim3 if you have $any$ questions regarding mathematics, openstudy user @dan815 will be more than glad to help you. He is the only mathematics helper on this site, so tell all your friends to tag him also! 
Good luck and happy studying!

anonymous · Answer

Ok, Thanks. So, any idea about the problem?

phi · Answer

The "dot product" for complex vectors is a generalized version of that for real-valued vectors. https://en.wikipedia.org/wiki/Dot_product#Complex_vectors Thus to get the correct value (of zero) you must start with the conjugated C(A^T) i.e. C(A^H), and then "unconjugate" it when you apply the (new and improved) definition of "dot product"

anonymous · Answer

That makes everything clear. Thanks a lot!