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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
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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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
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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