How to obtain the sum of squared eigenvalues without finding the eigenvalues?
How to obtain sum of square of eigenvalues without finding eigenvalues of a matrix?
Solution 1:
The eigenvalues of $A^2$ are the squares of the eigenvalues of $A$. The sum of the eigenvalues of any matrix (with algebraic multiplicity) is the trace. So the sum of the squares of the eigenvalues of $A$ (with algebraic multiplicity) is the trace of $A^2$.
Solution 2:
Trace of a Matrix is the sum of its Eigenvalues
Proof that the Trace of a Matrix is the sum of its Eigenvalues