mikeraj

I would appreciate it if someone could provide some helpful inputs to my original question. The equations in my question can be found in this reference Journal of Applied Physics 79, 7148 (1996). Thanks in advance.

I would appreciate it if someone could provide some helpful inputs to my original question. Thanks

Could you show one worked example? It will be easier for me to understand.

Hi zztop, The example in the link you gave did not show how the division involving two 1x3 matrices can be done. If I were to make the denominator into an inverse matrix and multiply it with the numerator, the problem would be the inverse for a 1x3 matrix cannot be determined (determinant cannot be calculated). Thanks

Could someone show me an example calculation of the Jacobian matrix in Eq. 16? I just need to understand the calculation steps. I highly appreciate it. Thanks!

My problem is not with the summation but on the partial differentiation in Eq 16

With reference to Eq. 16 in the attachment, I need help in understanding how the working is done to obtain the answers in Eq. 17. Eqs. 10, 11, and 15 are the inputs needed to solve Eg. 16. I am puzzled how a matrix could be differentiated with respect to another matrix. I would highly appreciate it if an example calculation can be shown. Thanks in advance! Equations.pdf

Hi HallsofIvy, I am clear now. Many thanks again!

I have a question regarding one example of eigenvector calculation. In Equation (1) of the attached example, should the first column of matrix A be written as 0.8x1 + 0.2x2 , rather than x1 + 0.2x2 ? Thanks in advance for your inputs. example.pdf

Hi HallsofIvy, thanks again. I understand it now. The solution is a basis vector of the eigenspace, which represents the multiples (infinite number) of the basis vector.

Hi Hallsoflvy, thanks for your inputs! If you take a look at the attachment, the solution given for [y z] is [2 -1]. Sorry as I am not familiar with latex, I typed the matrix in row form for convenience. example.pdf

My question here is not about eigenvalue or eigenvector. It is specific to the matrix equation I attached to my original post

I am reading a textbook on eigenvalue/eigenvector and this question is from there. Normally, I would use the method where the inverse of the matrix on the LHS is used to multiply the matrix on the RHS. However there are two issues here when trying to use this method. Firstly the RHS matrix is singular and the determinant cannot be found. Secondly any matrix multiplied with the zero matrix on the RHS will be zero anyway. The answer given in the book for [y z] is [2 -1]

For the attached matrix equation above, can someone guide me on the steps to solve it? Highly appreciate any guidance ! matrix equation.pdf