Any real normal matrix can be decompsed into two real symmetric matrices, with one invertible?
I know that each complex matrix can be decomposed into two complex symmetric matrices, with one invertible? How to do the real case?
2026-04-07 07:49:53.1775548193
Any real normal matrix can be decompsed into two real symmetric matrices, with one invertible?
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Since you know how to do it for complex: $A=B+iC+D+iE$, where $B+iC$ and $D+iE$ are symmetric (with real and complex parts separated) and at least one is invertible. Since $A$ is real, this implies $C=D=0$. So the result follows for real normal $A$.