Question: Let z = x + I y Cn. (a) Prove that, for the Hermitian dot product, ||z||2 = ||x||2 + ||y||2 (b) Does this

Let z = x + I y ∈ Cn.
(a) Prove that, for the Hermitian dot product, ||z||2 = ||x||2 + ||y||2
(b) Does this formula remain valid under a more general Hermitian inner product on Cn?

Step by Step Solution

★★★★★

3.44 Rating (167 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a b No for instance the formu... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

952-M-L-A-E (2100).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

A discrete random sequence is the input to a discrete linear filter h [n]. The output is Y [n]. Let Z [n] = X [n+ i] Y [n]. Find E [Z2 [n]], in terms of the autocorrelation functions for X [n] and Y...

(a) How would you define the angle between two elements of a complex inner product space? (b) What is the angle between (-1,2- i, -1 +2i)T and (-2- i.-i, 1 - i)T relative to the Hermitian dot product?

A complex matrix A is called normal if it commutes with its Hermitian transpose: AA = AAT. (a) Show that every real symmetric matrix is normal. (b) Show that every unitary matrix is normal. (c) Show...

\fCOMPLEX VARIABLES AND APPLICATIONS Eighth Edition James Ward Brown Professor of Mathematics The University of Michigan-Dearborn Ruel V. Churchill Late Professor of Mathematics The University of...

1 Multivariable functions and vector geometry Due date and time: Wednesday, June 7th at 9:30 AM in lecture Please ensure that you have read and understood the document \"Homework Guidelines" on the...

The Basics of Financial Mathematics Spring 2003 Richard F. Bass Department of Mathematics University of Connecticut c These notes are 2003 by Richard Bass. They may be used for personal use or class...

Math 636 Final - Quiz Component 1. The system of linear equations 2x2 x3 = 3 2x1 + x2 + 2x3 = 1 x1 + x2 + 3x3 = 2 (a) is consistent with a unique solution. (b) is consistent with infinitely many...

Math 104A Homework #3 Instructor: Lihui Chai General Instructions: Please write your homework papers neatly. You need to turn in both full printouts of your codes and the appropriate runs you made....

9/14/10 12:39 PM Page 381 Chapter dug84356_ch06a.qxd 6 Rational Expressions Advanced technical developments have made sports equipment faster, lighter, and more responsive to the human body. Behind...

The vertical component of the acceleration of a sailplane is zero when the air pushes up against its wings with a force of 3.0 kN. (a) Assuming that the only forces on the sailplane are that due to...

1. Using common sense, determine a Muther grid for the departments. 2. Determine the location of the departments on a 200 ft long by 150 ft wide floor plan. Locate the receiving area on the top and...

sole this CHALLENGE ACTIVITY 4.5.1: Composition of functions. 632724.4957092.qx3zqy7 Start Given: N f(xx) = x+4 9(x) =6.x 3 (fog)(0) = Ex: 15 4 5 1 2 3 4 5 Check Next Feedback

What does Justice Cardozo find about proximate cause?

By inspection, determine whether the linear operator is one-to-one. (a) The orthogonal projection on the x-axis in R2. (b) The reflection about the y-axis in R2.

Use Theorem 4.3.3 to find the standard matrix for T: R2 R2 from the images of the standard basis vectors. (a) T: R2 R2 projects a vector orthogonally onto the x-axis and then reflects that vector...

Use the result in Example 6 to find the orthogonal projection of x onto the line through the origin that makes an angle 0 with the positive x-axis. x = (- 1, 2); = 45

Question 1: Suppose that you have the following interest rates: Time period (Years) Spot rate Forward rate Expected future single year spot rate 1 8.00 2 8.75 ((1+8.75)/(1+8))-1=9. 56 3 9.33...

Rebalancing a portfolio is performed in response to changes in the economic environment, in the life cycle of the client, or to re-establish the initial asset mix. Which of the following would...

question 24 India's Current Account. Use the following balance of payments data for India from the IMF: What is India's current account balance for years 2006, 2008, and 2011? The current account...