Exercise 6.4: Inequality for Matrix Exponential

chapter 6

Take the eigendecomposition \(A = Q \Lambda Q^\top\), and observe \(I + A = Q (I + \Lambda) Q^\top \, .\) Since \(1 + x \leq e^x\) \begin{align} I + A \preceq Q e^{\Lambda} Q^\top = e^{A} \, . \end{align}