kemfys

Hi taeto, Thank you for kind response. I am not a mathematician, so I am not sure how to respond to the question based on ring. I am a physical chemist and I have some problem with me for which I am trying to develop a model using matrices. And my model requires that multiplication between two parameters be non-commutative and therefore I have chosen matrices. And to preserve the uniqueness in the result of matrix multiplication between tow matrices, I have chosen the multiplication to be outer product. Therefore, it is I who defined x⊗y = b and y⊗x = c. And the matrices x and y are 2×2 matrices. Actually, the intention is to extend it to any dimension. Please let me know if I am not clear. Thank you

Suppose I have a matrix P = \begin{bmatrix}x⊗x&x⊗y\\y⊗x&y⊗y\end{bmatrix} which is equal to another matrix Q = \begin{bmatrix}a&b\\c&d\end{bmatrix}. Is it possible to solve for x and y. Since xy and yx are equal to b and c and are not the same, the elements in the matrix P are outer product of two matrices x and y. Is it possible to solve for x and y such that xy and yx can be made predictable. Kindly let me know if I am not clear. Thank you for the kind help.

How do we find the what kind of electronic transition it is for a molecule computationally? How do we arrive at any of the following transition for any UV-Vis spectroscopy of organic molecules. σ → σ*π → π*n → σ*n → π* Can someone please tell me how it is done.