Question: Let A, B n (C) such that A is normal and B is hermitian Prove that ||AB|| = ||BA||

Let A, B ∈ μn (C) such that A is normal and B is hermitian Prove that ||AB|| = ||BA||


Step by Step Solution

★★★★★

3.42 Rating (155 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
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 (2 attachments)

PDF file Icon

60929a33b213f_209425.pdf

180 KBs PDF File

Word file Icon

60929a33b213f_209425.docx

120 KBs Word File

Students Have Also Explored These Related Mathematics Questions!

Q:

Prove that if AB and BA are both defined, then AB and BA are both square matrices.

Q:

A and B are Hermitian operators and AB BA = iC. Prove that C is a Hermitian operator

Q:

Let B be an n x n matrix. Suppose AB = 0 for some nonzero m n matrix A. Show that no n n matrix C exists such that BC = I.

Q:

Let A and B be nonzero n n matrices such that A is symmetric and B is skew-symmetric. Prove that {A, B} is linearly independent.

Q:

(a) Let A be a 2 x 2 matrix such that tr A = 0 and = det A > 0. Prove that eA = (cos ) I + sin / A. Use Exercise 8.2.51. (b) Establish a similar formula when det A

Q:

Let D be an unbounded domain of f and let {x_n} be a sequence in D such that lim_(n->infinity) x_n = infinity and lim_(n->infinity) f(x_n) = L. Prove lim_(n->infinity) f(x) = L.

Q:

Let A be a positive constant. Let f be a function such that f( 7r) = 5 and f'(7) = 2 . If g(x) = In((f(x) )2 + A sin a), then g' (TT) equals O1 O1 25 25 - A 25 20 - A 25 10 + A 25Let f be a function...

Q:

Question 1 (1 point) A box with square base of length x and height y is changing shape such that dr - 3cm/s, - 7cm/s. Find the rate of change of volume when x = 2cm, y = 4cm. Recall: the volume V of...

Q:

This question is designed to be answered without a calculator. The area under the curve f(x) = sin X + cos x over the interval [ %,%] is This question is designed to be answered with a An...

Q:

Let 0 be an angle such that sin 0 = 8 and cote Let 9 be an angle such that sino and coto

Q:

Based on the following data for Scout Company, determine the contribution margin. Sales are 1,500 units, sales price is $7, variable costs are $3. 25 per unit, and fixed costs total $3,000.

Q:

Q2a) Better Health Hospital- Income Statement (2018/19 Financial Year) *Note: All figures in $'000* Q2b) Better Health Hospital- Balance Sheet (2018/19 Financial Year) *Note: All figures in $'000*...

Q:

50 units @ $106 60 units @ $118 20 units @ $126 70 units @ $130 There are 80 units of the item in the physical inventory at December 31. The periodic inventory system is used. Determine the inventory...

Q:

During FY 2018, Adelphi Company reported sales of $400,000, a contribution margin of $5.00 per unit, fixed costs of $90,000, and net income of $20,000. Use this information to determine the number of...

Q:

[Combinatorics, Conditional Probability and Beyond] Consider a game with n = N participants which are somehow ordered (P1, P2, ..., Pn). The game starts with the first numbered player (P1) tosses a...

Q:

Corruption has been a significant problem in Iraq. Opening and running a business in Iraq usually requires paying multiple bribes to government officials. We can think of there being a demand and...

Q:

ti Question 2 (14 pts.) to d Consider the simultaneous move game between a taxpayer and a tax inspector. The taxpayer chooses whether or not to underreport his taxable income. The tax auditor chooses...

Q:

Evaluate each logarithm to four decimal places. log 0.257

Q:

If n Z+ and n >2 prove that 0 (mod n), odd (mod n), n even.

Q:

Suppose the probability that the integer key is in the array a1, a2, a3, ..., an (of ft distinct integers) is 3/4 and that each array element has the same probability of containing this value. If the...

Q:

The four input lines for the gating network shown in Fig. 15.12 provide the binary equivalents of the numbers 0, 1, 2, ..., 15, where each number is represented as abce, with e the least significant...

Q:

Consider the market represented in Figure 5P-5. a. Draw the consumer surplus and producer surplus if the market is functioning at the equilibrium price and quantity. Compute the total surplus if the...

Q:

Consider the market represented in Figure 5P-4. a. Calculate total surplus when supply is S1. b. Calculate total surplus when supply increases to S2.

Q:

Answer the following questions based on Tables 5P-1 and 5P-2. a. What is the quantity demanded at $10? What is the quantity supplied at $10? b. What is the quantity demanded at $25? What is the...