MHB Finding the Inverse of Symmetric Matrices with Non-Real Coefficients

[OhMyMarkov]

Hello everyone!

I'm struggling to find a general formula for obtaining an inverse of a symmetric matrix, for e.g.

1 i -1
i -i 2
-1 2 1

Any help is appreciated!

 

[Sudharaka]

Hello everyone!

I'm struggling to find a general formula for obtaining an inverse of a symmetric matrix, for e.g.

1 i -1
i -i 2
-1 2 1

Any help is appreciated!

Hi OhMyMarkov, :)

Are you specifically concerned about 3x3 symmetric matrices? The general form of the inverse of a 3x3 matrix is given >>here<<. For a symmetric matrix \(b=d,\,c=g\mbox{ and } f=h\).

Kind Regards,
Sudharaka.

 

[OhMyMarkov]

Hello Sudharaka!

Well, I'm actually interested in symmetric matrices that have this shape (the given example is for a 3x3 matrix):

1 1 1
1 2 4
1 4 16Note that the coefficients need not be real.