Let C2,2 be the set of 2 × 2 matrices with complex coefficients, and define the map a 0 T: C2,2 C2,2 by T ([]). where a is the complex conjugate of a. = 0 b - C " (a) Show that for any À € R, and any A ≤ C²,², T(\A) = XT(A). (b) Find a value λ E C and a matrix A E C²,2 such that T(AA) ‡ XT(A).
Let C2,2 be the set of 2 × 2 matrices with complex coefficients, and define the map a 0 T: C2,2 C2,2 by T ([]). where a is the complex conjugate of a. = 0 b - C " (a) Show that for any À € R, and any A ≤ C²,², T(\A) = XT(A). (b) Find a value λ E C and a matrix A E C²,2 such that T(AA) ‡ XT(A).
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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![Let C2,2 be the set of 2 × 2 matrices with complex coefficients, and define the map
where a is the complex conjugate of a.
0
T: C²,2 → C²,2 by T
([d]) = [bº].
0
(a) Show that for any λ = R, and any A € C²,², T(\A) = XT(A).
(b) Find a value À E C and a matrix A € C²,² such that T(\A) ‡ \T(A).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe60e14a8-856f-447c-ac90-795ae43e00b4%2F78e04907-5f20-43c6-906c-5e667bbb6cf1%2F9v8zrlp_processed.png&w=3840&q=75)
Transcribed Image Text:Let C2,2 be the set of 2 × 2 matrices with complex coefficients, and define the map
where a is the complex conjugate of a.
0
T: C²,2 → C²,2 by T
([d]) = [bº].
0
(a) Show that for any λ = R, and any A € C²,², T(\A) = XT(A).
(b) Find a value À E C and a matrix A € C²,² such that T(\A) ‡ \T(A).
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