Next questionShow that if A is both diagonalizable and invertible, then so is A'......What does it mean if A is diagonalizable?O A.If A is diagonalizable, then A = PDP- 1for some invertible P and diagonal D.В.- 1If A is diagonalizable, then AK =PDP¯ for some invertible P and diagonal D.%3DC. If A is diagonalizable, then A = PD for some invertible P and diagonal D.O D. If A is diagonalizable, then A must be a triangular matrix.

Introduction: If matrix A is an invertible matrix then every eigenvalue of this matrix non-zero.

Answered: Show that if A is both diagonalizable…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Exercise 4.2.7 Explicitly calculate the commutator of the operators of Example 4.2.2.
Let A find on Conditions a,b.c and d that AX =0 has has infinitely many solution . what must there Pere be true about a,b,c and d in order for A to be invertible ?
Explain and find h so that (if h exists) so that a. T(x) = Ax is one-to-one b. T(x) = Ax is onto 2 6 [X] h 3 A= Find & so that B- a 80 B= m) x + ( + h Sta to 13 2 a -1 2 an a ooo is invertible
Let A E BL(H). Then A is called normal if A*A = AA*, uni- tary if A*A = I = AA*, that is, A* = A-¹, and self-adjoint if A* = A. Clearly, if A is unitary or self-adjoint, then A is normal. How- ever, a normal operator need be neither unitary nor self-adjoint. For example, let H = K² and for x = (x(1), x(2)) in H, A(x) = (x(1) − x(2), x(1) + x(2)). Then it can be easily seen that for x = H, A*(x) = (x(1) + x(2), −x(1) + x(2)), Request A*A(z) = 2(x(1),z(2)) = AA*(x). Hence A*A = AA*, but A*A# I and A* ‡ A. explain these steps in détail.
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Show that if A is both diagonalizable and invertible, then so What does it mean if A is diagonalizable? O A. If A is diagonalizable, then A = PDP¯1 for some inve OB. If A is diagonalizable, then AK = PDP¯1 for some in