Find the transpose, conjugate, and adjoint of 6-3i 2+12i -19i 0 5+2.1i 17 1 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
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Find the transpose, conjugate, and adjoint of
(i) Transpose is idempotent: (4¹) = A.
(ii) Transpose respects addition: (A + B) = A¹+ B¹.
(iii) Transpose respects scalar multiplication: (c. A)¹ = c A.
These three operations are defined even when m‡n. The transpose and adjoint are both functions from CX to Cxm
These operations satisfy the following properties for all c E C and for all A, B € CX".
(iv) Conjugate is idempotent: A = A.
(v) Conjugate respects addition: A
6-3i
0
1
B = A + B
(vi) Conjugate respects scalar multiplication: C. A = c. A.
(vii) Adjoint is idempotent: (4†)t = 4.
(viii) Adjoint respects addition: (A + B) =A+B+.
(ix) Adjoint relates to scalar multiplication: (CA)t = c · At
2 + 12i
5+2.1i
2+5i
-19i
17
3-4.5i
Transcribed Image Text:Find the transpose, conjugate, and adjoint of (i) Transpose is idempotent: (4¹) = A. (ii) Transpose respects addition: (A + B) = A¹+ B¹. (iii) Transpose respects scalar multiplication: (c. A)¹ = c A. These three operations are defined even when m‡n. The transpose and adjoint are both functions from CX to Cxm These operations satisfy the following properties for all c E C and for all A, B € CX". (iv) Conjugate is idempotent: A = A. (v) Conjugate respects addition: A 6-3i 0 1 B = A + B (vi) Conjugate respects scalar multiplication: C. A = c. A. (vii) Adjoint is idempotent: (4†)t = 4. (viii) Adjoint respects addition: (A + B) =A+B+. (ix) Adjoint relates to scalar multiplication: (CA)t = c · At 2 + 12i 5+2.1i 2+5i -19i 17 3-4.5i
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