Reference no: EM13894718
1. Consider R3with two orthonormal bases: the canonical basis e=(e1,e2,e3) and the basis f=(f1,f2,f3), where
f1=(1,1,1)/(3^(1/2)) ,f2=(1,-2,1)/(6^(1/2)) ,f3=(1,0,-1)/(2^(1/2))
Find the canonical matrix, A, of the linear map T∈?(R3) with eigenvectors f1,f2,f3 and eigenvalues 1, 1/2, -1/2, respectively.
2. For the following matrices, verify that A is Hermitian by showing that A=A∗ ,?nd a unitary matrix U such that U-1AU is a diagonal matrix, and compute exp(A).
A = 5 0 0
0 -1 -1 + i
0 -1 - i 0
3. For the following matrices, either ?nd a matrix P (not necessarily unitary) such that P-1AP is a diagonal matrix, or show why no such matrix exists.
A =5 0 0
1 5 0
0 1 5
4.Let V be a finite-dimensional vector space over F, and suppose that S, T ∈ L(V ) are positive operators on V . Prove that S + T is also a positive operator on T.
|
In many countries the central bank is prepared
: 1.A country's central bank (e.g. the Bank of England or the US Federal Reserve Bank) has a key role in ensuring the stability of the banking system.
|
|
What the formula for the circumference of a circle
: What's the formula for the circumference of a circle?
|
|
Make no additional deposits or withdraws
: If you put $ 2,000 in a savings account that pays 6% interest compounded continuously, how much money will you have in your account in 4 years? Assume you make no additional deposits or withdraws. A: $2,983.65 B: $2,542.50
|
|
Use newton''s law of cooling
: You place a cup of 210°F coffee on a table in a room that is 68°F, and 10 minutes later, it is 200°F . Approximately how long will it be before the coffee is 180°F? Use Newton's law of cooling: 180°F A: 1 hour B: 15 minutes
|
|
R3with two orthonormal base
: 1. Consider R3with two orthonormal bases: the canonical basis e=(e1,e2,e3) and the basis f=(f1,f2,f3), where f1=(1,1,1)/(3^(1/2)) ,f2=(1,-2,1)/(6^(1/2)) ,f3=(1,0,-1)/(2^(1/2))
|
|
Normal good, an inferior good and a giffen good
: 1.Distinguish between a normal good, an inferior good and a Giffen good. Use indifference curves to illustrate your answer.
|
|
Using MACRS depreciation method
: Casa Grande Farms is considering purchasing multiple tractors for a total purchase price of $540,000. These tractors are expected to generate EBITDA of $250,000 for each of the next three years. Assuming that Casa Grande Farms depreciates these tract..
|
|
Difference between connectionless and connection-oriented
: How does SSH differ from Telnet? How does HTTPS differ from HTTP?
|
|
The npv for upgrading to the new grill is closest to
: Two years ago the Krusty Krab Restaurant purchased a grill for $50,000. The owner, Eugene Krabs, has learned that a new grill is available that will cook Krabby Patties twice as fast as the existing grill. If the Krusty Krab's opportunity cost of cap..
|