10. Suppose that Ja) - En, a«|k), [3) = E bu |k). Show that %3D and that this means that the matrix representation in the given orthonormal basis satisfies la)(3) = ab', where a= a.]", b = [b, ... ...

10. Suppose that Ja) - En, a«|k), [3) = E bu |k). Show that %3D and that this means that the matrix representation in the given orthonormal basis satisfies la)(3) = ab', where a= a.]", b = [b, ... ...

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.6: Matrices

Problem 21E: Suppose that A is an invertible matrix over and O is a zero matrix. Prove that if AX=O, then X=O.

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Question

10. Suppose that |a) = E"-1 ax|k), |B) = E"-, bu|k). Show that
(la)(8|)aj = a,b,,
and that this means that the matrix representation in the given orthonormal basis satisfies
|a)(3| = a b°,
where a= [a
a,]", b= [b,
..

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