User:IssaRice/Linear algebra/Trace of matrix equals sum of eigenvalues

This is chapter 4 exercise 1.11 in Linear Algebra Done Wrong (p. 105).

Theorem. Let $A$ be a matrix. Then $\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{e}A={\lambda }_1+\cdots +{\lambda }_n$, where ${\lambda }_1,\dots ,{\lambda }_n$ are the eigenvalues of $A$ (counting multiplicities).

Proof. We already know that $det(A-\lambda I)=({\lambda }_1-\lambda )\cdots ({\lambda }_n-\lambda )$.

See also

• https://machinelearning.subwiki.org/wiki/User:IssaRice/Linear_algebra/Determinant_of_matrix_equals_product_of_eigenvalues