Exercise 2.2.5 Find the transpose, conjugate, and adjoint of 6-3i 2+12i 0 1 -19i 5+2.1i 17 2+5i 3-4.5i
Exercise 2.2.5 Find the transpose, conjugate, and adjoint of 6-3i 2+12i 0 1 -19i 5+2.1i 17 2+5i 3-4.5i
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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Question
![Exercise 2.2.5 Find the transpose, conjugate, and adjoint of
(i) Transpose is idempotent: (4¹) = A.
(ii) Transpose respects addition: (A + B) = A + BT.
(iii) Transpose respects scalar multiplication: (c. A)¹ = c · A¹.
These three operations are defined even when m‡ n. The transpose and adjoint are both functions from Cxn
These operations satisfy the following properties for all c E C and for all A, B € Cmx".
to Cnxm
(iv) Conjugate is idempotent: A = A.
(v) Conjugate respects addition: A + B = A + B
(vi) Conjugate respects scalar multiplication: C. A = c. A.
(vii) Adjoint is idempotent: (4†) = 4.
(viii) Adjoint respects addition: (A + B) =A† + B†.
(ix) Adjoint relates to scalar multiplication:
6-3
0
1
(c. A)* = c. At
2 + 12i
-19i
5+2.1i
17
2 + 5i 3-4.5i](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0f7775f3-edad-4f27-ba1b-f7886a7505bd%2Ffea99392-72b2-4545-a267-63907a4e73fb%2F947ykd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Exercise 2.2.5 Find the transpose, conjugate, and adjoint of
(i) Transpose is idempotent: (4¹) = A.
(ii) Transpose respects addition: (A + B) = A + BT.
(iii) Transpose respects scalar multiplication: (c. A)¹ = c · A¹.
These three operations are defined even when m‡ n. The transpose and adjoint are both functions from Cxn
These operations satisfy the following properties for all c E C and for all A, B € Cmx".
to Cnxm
(iv) Conjugate is idempotent: A = A.
(v) Conjugate respects addition: A + B = A + B
(vi) Conjugate respects scalar multiplication: C. A = c. A.
(vii) Adjoint is idempotent: (4†) = 4.
(viii) Adjoint respects addition: (A + B) =A† + B†.
(ix) Adjoint relates to scalar multiplication:
6-3
0
1
(c. A)* = c. At
2 + 12i
-19i
5+2.1i
17
2 + 5i 3-4.5i
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