Find the transpose, conjugate, and adjoint of 6-3i 2+12i -19i 0 5+2.1i 17 1 2+5i 3-4.5i
Find the transpose, conjugate, and adjoint of 6-3i 2+12i -19i 0 5+2.1i 17 1 2+5i 3-4.5i
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.6: The Algebra Of Matrices
Problem 39E
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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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