Algebra - inverse of complex numbers

[bemigh]

Hey, i have an algebra question. I have the matrix
0.3 0.3 0.3
0.4 0.4 0.5
0.3 0.2 0.3
Now, i need to find the eigenvectors for this. However, when i did this, i got complex numbers. I need to find the inverse of this matrix, is there a way to take the inverse a matrix with complex numbers? or did i do something wrong along the way??
Cheers

 

[dextercioby]

I don't know if u did something wrong along the way,i'm not going to do the arithmetics for you.I'll just tell you that there is no problem with inverting a matrix from $$\mathcal{M}_{3}(\mathbb{C})$$...As long as the determinant is nonzero,of course...

Daniel.

 

[thepatientmental]

Hi there,

First of all, great job on finding the eigenvectors for the matrix! It is not uncommon to get complex numbers as eigenvectors, especially for matrices with non-real eigenvalues.

To find the inverse of a matrix with complex numbers, we can use the same process as finding the inverse of a real number matrix. The only difference is that we need to use the complex number operations, such as conjugates and complex division.

In your case, you can follow these steps to find the inverse of the matrix:

1. Find the determinant of the matrix. If you are not familiar with finding determinants of 3x3 matrices, you can use an online calculator or software to help you.

2. Take the conjugate of each element in the matrix. For example, the conjugate of 0.3 is 0.3 and the conjugate of 0.4+0.5i is 0.4-0.5i.

3. Replace each element with its conjugate and divide by the determinant found in step 1. This will give you the adjugate matrix.

4. Finally, take the transpose of the adjugate matrix to get the inverse of the original matrix.

I hope this helps! Let me know if you have any further questions. Good luck!