Answer by G Cab for Geometric interpretation of a hollow symmetrical 3D matrix
What you are proposing is and additive transformation of coordinates.$$\mathbf{A} = diag\left( \mathbf{A} \right) + hollow\left( \mathbf{A} \right) $$corresponds to thatthe new vector $\mathbf{x}' =...
View ArticleAnswer by G Cab for Geometric interpretation of a hollow symmetrical 3D matrix
Just as a note aside, if instead of making it hollow, you fill the diagonal with $f_{1,\,2,\,3} (a,b,c)$then you can get some significant factorization. For example:$$\left( {\begin{array}{*{20}c} 1...
View ArticleGeometric interpretation of a hollow symmetrical 3D matrix
Any matrix $A$ can be presented as a sum of its symmetrical and skew-symmetrical part: $A=sym(A)+skew(A)$. Decomposition can go further and we can present symmetrical part as a sum of some diagonal...
View ArticleAnswer by H. D. for Geometric interpretation of a hollow symmetrical 3D matrix
I would say that much like skewsymmetric matrices, symmetric hollow matrices have a similar geometrical/group theoretical interpretation.Start from dimension $d = 2$, then the only symmetric hollow...
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