Why sqrt 2 in the eigen

I am redoing some matrices that deal with interactive relationships and this can relate to anything, even Haar-like stuff, springs, heat flows, material stress, current or any linear process relationship. What I wanted to understand is why 2-sqrt(2), 2, and 2+(sqrt(2) [ 2-√2,2,2+√2] show up as terms in the eigen values. The trace or 2+2+2 = their sum and this is correct and the det(K) is properly computed. Perhaps I am looking too deep into this. I know there is a deeper relationship, but it has eluded me throughout the matrix analysis study and this is why I am going over it again with all the possible variations of its application. It has to do with dimensionality itself and perhaps I am just not able to grasp it as it is too complex for my mind. I had hoped that some really simple examples would make it easier to see.

I am glad that octave has A'=transpose(A) because that would be a real pain to type every time it was used. I almost thought that √2 was π and that has happened to me before and I thought I found some deep relationship to trigonometric relationships and it is just way too easy to (dyslexia)' 3.14 to 3.414 when I am thinking about something else.


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