- #1
ekkilop
- 29
- 0
Hi folks!
I've encountered the matrix below and I'm curious about its properties;
[tex] R=
\begin{pmatrix}
0 & N-S\\
N+S & 0
\end{pmatrix}
[/tex]
where R, N and S are real matrices, R is 2n by 2n, N is n by n symmetric and S is n by n skew-symmetric.
Clearly R is symmetric so the eigenvalues are real, but what else can be said about a matrix of this type? I checked through some literature but didn't really know what to look for. Surely the form is simple enough that it should have been studied.
In a special case, the elements of the rows of the matrix N+S sum to zero. Could this affect the properties somehow?
Any ideas would be much appreciated!
I've encountered the matrix below and I'm curious about its properties;
[tex] R=
\begin{pmatrix}
0 & N-S\\
N+S & 0
\end{pmatrix}
[/tex]
where R, N and S are real matrices, R is 2n by 2n, N is n by n symmetric and S is n by n skew-symmetric.
Clearly R is symmetric so the eigenvalues are real, but what else can be said about a matrix of this type? I checked through some literature but didn't really know what to look for. Surely the form is simple enough that it should have been studied.
In a special case, the elements of the rows of the matrix N+S sum to zero. Could this affect the properties somehow?
Any ideas would be much appreciated!