Recent content by Ismail Siddiqui

@andrewkirk @micromass I wrote it out in component form and re-arranged it from there. Worked out perfectly.Thanks again!

oh boy, your absolutely right. I completely forgot to add on the complex conjugate. It should be ∑vi* wi.

I'll try it that way and see where I get, thanks.

v ⋅ w = ∑ viwi where vi and wi are the ith entries of the vectors v and w and 1 ≤ i ≤ n where n is the last index.

@micromass The LHS and RHS of the equations are defined by the vector dot product, I've made some changes in the original post in an attempt to clarify that. @andrewkirk I've added more to the relevant equations sections to address what you said. There are probably a few more theorems but this...

Homework Statement Let A be an n x n matrix, and let v, w ∈ ℂn. Prove that Av ⋅ w = v ⋅ A†w Homework Equations † = conjugate transpose ⋅ = dot product * = conjugate T = transpose (AB)-1 = B-1A-1 (AB)-1 = BTAT (AB)* = A*B* A† = (AT)* Definitions of Unitary and Hermitian Matrices Complex Mod...