2.5-2. Let (Z,) be a symplectic vector space. Let A: Z Z be a linear...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
2.5-2. Let (Z,) be a symplectic vector space. Let A: Z → Z be a linear map and assume that (IA) is invertible. Show that A is Hamiltonian if and only if its Cayley transform (I + A)(I - A)-¹ is symplectic. Give an example of a linear Hamiltonian vector field such that (IA) is not invertible. 2.5-2. Let (Z,) be a symplectic vector space. Let A: Z → Z be a linear map and assume that (IA) is invertible. Show that A is Hamiltonian if and only if its Cayley transform (I + A)(I - A)-¹ is symplectic. Give an example of a linear Hamiltonian vector field such that (IA) is not invertible.
Expert Answer:
Answer rating: 100% (QA)
Ans vector Space Cz2 Then X Hfor DA 2 is 2iskew define ... View the full answer
Related Book For
Posted Date:
Students also viewed these physics questions
-
Let Z be a standard normal random variable. Use Appendix Table A.1 to find the numerical value for each of the following probabilities. Show each of your answers as an area under fZ(z). (a) P(0 Z ...
-
Give an example of a series such that converges but an lan! diverges.
-
Give an example of how a hospital, such as the Mayo Clinic, might use job-order costing concepts.
-
Let y vary directly with x. Complete the following. Find y when x = 1, if y = when x = 3.
-
Raleigh Corp. has an investment with a carrying value (equity method) on its books of $170,000 representing a 30% interest in Borg Company, which suffered a $620,000 loss this year. How should...
-
Bellingham Company produced 15,000 units of product that required 4 standard direct labor hours per unit. The standard variable overhead cost per unit is $0.90 per direct labor hour. The actual...
-
FHA Loan Company has 10,000 shares of \($3.50,\) no-par preferred stock and 50,000 shares of no-par common stock outstanding. FHA declared and paid the following dividends during a three-year period:...
-
Below is a project WBS with cost apportioned by percents. If the total project cost is estimated to be $600,000, what are the estimated costs for the following deliverables? a. Design? b....
-
1.Bulletin board - does the company have to allow union flyers?
-
The Springfield School Board has made the decision to close one of its middle schools (sixth, seventh, and eighth grades) at the end of this school year and reassign all of next year's middle school...
-
An ellipsoid with principal axis of lengths 2a, 2a and 2b is magnetized uniformly in a direction parallel to the 2b-axis. The magnetization of the ellipsoid is Mo. Find the magnetic pole densities...
-
ABC Hedge Fund had a 2% return when the market returned 10%. However, ABC's Sharpe ratio was superior to that of the market benchmark. What is the significance of the Sharpe ratio?
-
5. What will $82,000 grow to be in 11 years if it is invested today at 8% and the interest rate is compounded monthly?
-
Henry, aged 25, believes in the efficient-market hypothesis. He has just graduated from college and works part-time. He regularly invests $100 every two weeks when he is paid. His objective is...
-
ABC Canadian Equity ETF constantly screens the market for securities that at a discount to book value, have dividends yields higher than the market average, and have betas below 1. What type of ETF...
-
Discus the step a firm souls before investing I Information technology tool s and the consideration such a firm should make when selecting it tools?
-
What motive is there for society as a whole to support whistleblowing? a . ) Qui tam provisions b . ) Civil penalties supporting the federal government c . ) Additional SEC oversight d . ) Reducing...
-
Draw and label the E and Z isomers for each of the following compounds: 1. CH3CH2CH==CHCH3 2. 3. 4. CH,CH2C CHCH2CH Cl CH3CH2CH2CH2 CH CH2CCCH2CI CHCH3 CH3 HOCH CH CCC CH O-CH C(CH
-
Find the equation of the parabola y = ax2 + bx + c that goes through the points (1,6), (2, 4), (3, 0).
-
Answer Exercise 5.5.30 when f(t) = sin t. Use a computer to numerically evaluate the integrals. Exercise 5.5.30 Find the best cubic approximation to f(t) = e' based on the L2 norm on [0, 1].
-
The commutator of two matrices A, B, is defined to be the matrix C = [A.B] = AB - BA. (1.12) (a) Explain why [A.B] is defined if and only if A and B are square matrices of the same size. (b) Show...
-
You have been approached by promoters to give an opinion on the financial statements to be included in the prospectus of a proposed corporation to be named U-Park Corporation. U-Park will own and...
-
The following questions relate to the auditor's responsibility for reporting on inconsistency of application of accounting principles. Select the best response. a. Raider uses the last-in, first-out...
-
J.O. Cole, a sole proprietor, operates a trucking business. Cole also has assets and liabilities in connection with other activities. You are retained to audit the accounts of the J.O.C. Truck Lines...
Study smarter with the SolutionInn App