Functions of matrices are typically defined by their Taylor series expansions. For example, (a) Find exp (M),
Question:
Functions of matrices are typically defined by their Taylor series expansions. For example,
(a) Find exp (M), if
(b) Show that if M is diagonalizable, then
Comment: This is actually true even if M is not diagonalizable, but it’s harder to prove in the general case.
(c) Show that if the matrices M and N commute, then
Prove (with the simplest counterexample you can think up) that Equation A.101 is not true, in general, for non-commuting matrices.
(d) If H is hermitian, show that eiH is unitary.
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Related Book For
Introduction To Quantum Mechanics
ISBN: 9781107189638
3rd Edition
Authors: David J. Griffiths, Darrell F. Schroeter
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