Quiz dossier / The Matrix Cookbook

10 - Functions and Operators

Advanced formula selection, assumption checking, and exact application for Functions and Operators, book pages 58-63.

9 questionsEstimated 36 min0 flagged

Session status

Draft

Question 1

4 point(s)

Matrix functions and power series

Let a scalar function have a convergent power series on the spectrum/domain of $A$ .

Valid	Invalid	Statement
		The corresponding matrix function can be defined by substituting powers of $A$
		$e^A=I+A+A^2/2!+\cdots$
		$e^{A+B}=e^Ae^B$ for arbitrary noncommuting $A,B$
		Diagonalization can reduce a matrix function to scalar functions of eigenvalues when valid