(a) (b) Let V = F" and let A EMnxn (F), F is complex field. Prove that (x, y) = (4¹x, y) for all x, y eV. Suppose that for some B Mnx(F), we have (x, y) = (Bx, y) for all x, y €V. Prove that B=A*.
(a) (b) Let V = F" and let A EMnxn (F), F is complex field. Prove that (x, y) = (4¹x, y) for all x, y eV. Suppose that for some B Mnx(F), we have (x, y) = (Bx, y) for all x, y €V. Prove that B=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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Please Help A and B
Transcribed Image Text:4.
(a)
(b)
Let V = F" and let A EM(F), F is complex field.
Prove that (x, Ay) = (4x, y) for all x, y €V.
Suppose that for some B =Mnx(F), we have (x, Ay) = (Bx, y) for all x, y EV. Prove that
B=A*.
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