$A$ is a $p\times p$ real matrix and $\lambda_{i}$ are its eigenvalues. $\operatorname{tr}(A)$ is the trace of $A$.
How to geometrically interpret $\sum^{p}_{1}\lambda_{i}(A)=\operatorname{tr}(A)$?
I have learnt linear algebra for two semesters. I knew the basic concepts of trace and eigenvector.
The answer in the mathoverflow interprets geometrical meaning of trace.But,how to interpret the trace is equal to the sum of eigenvalue geometrically?