Question
Suppose A is a real 2x2 matrix with complex eigenvalues α ± i β , β...
Suppose A is a real 2x2 matrix with complex eigenvalues α ± i β , β ≠ 0. It was shown in class that the corresponding eigenvectors will be complex. Suppose that a + i b is an eigenvector for α + i β , for some real vectors a , b . Show that a − i b is an eigenvector corresponding to α − i β . Hint: properties of the complex conjugate may be useful. Please show all work, Thanks
Homework Answers
Answer #1
Not the answer you're looking for?
Similar Questions
Suppose A is a 2x2 matrix whose eigenvalues all have negative real parts. For the system...
Suppose A is a 2x2 matrix whose eigenvalues all have negative
real parts. For the system x 0 = Ax, is the origin stable or
unstable?
5. Suppose A is an n × n matrix, whose entries are all real numbers, that...
5. Suppose A is an n × n matrix, whose entries are all real
numbers, that has n distinct real eigenvalues. Explain why R n has
a basis consisting of eigenvectors of A. Hint: use the “eigenspaces
are independent” lemma stated in class.
6. Unlike the previous problem, let A be a 2 × 2 matrix, whose
entries are all real numbers, with only 1 eigenvalue λ. (Note: λ
must be real, but don’t worry about why this is true)....
Let X ∼ Beta(α, β). (a) Show that EX 2 = (α + 1)α (α +...
Let X ∼ Beta(α, β).
(a) Show that EX 2 = (α + 1)α (α + β + 1)(α + β) .
(b) Use the fact that EX = α/(α + β) and your answer to the
previous part to show that Var X = αβ (α + β) 2 (α + β + 1).
(c) Suppose X is the proportion of free-throws made over the
lifetime of a randomly sampled kid, and assume that X ∼ Beta(2,
8)
....
1. Given β = XT 1×nAn×nXn×1, show that the gradient of β with respect to X...
1. Given β = XT 1×nAn×nXn×1, show that the gradient of β with
respect to X has the following form: ∇β = X T (A + A T ). Also,
simplify the above result when A is symmetric. (Hint: β can be
written as Pn j=1 Pn i=1 aijxixj ).
2. In this problem, we consider a probabilistic view of linear
regression y (i) = θ T x (i)+ (i) , i = 1, . . . , n, which...
Suppose the following data were obtained from the admissions office of a 2-year junior college. Of...
Suppose the following data were obtained from the admissions
office of a 2-year junior college. Of the first-year class (F), 75%
became sophomores (S) the next year and 25% dropped out (D). Of
those who were sophomores during a particular year, 90% graduated
(G) by the following year and 10% dropped out.
(a) [8 pts] Set up a Markov chain transition matrix with states
D, F, G, and S that describes the scenario. Hint: Although not
explicitly stated, you can...
1) Describe an example of each of the following that may be found of your kitchen:...
1) Describe an example of each of the following that may be
found of your kitchen: Explain how your choice falls into this
category, and if there is a chemical name or symbol for it, provide
that as well. Provide a photo of your example with your ID card in
it. a) a compound b) a heterogeneous mixture c) an element (symbol)
Moving to the Caves… Lechuguilla Caves specifically. Check out this
picture of crystals of gypsum left behind in...
ADVERTISEMENT
Need Online Homework Help?
Get Answers For Free
Most questions answered within 1 hours.
ADVERTISEMENT
Active Questions
asked 5 minutes ago
asked 15 minutes ago
asked 23 minutes ago
asked 37 minutes ago
asked 49 minutes ago
asked 1 hour ago
asked 1 hour ago
asked 1 hour ago
asked 1 hour ago
asked 1 hour ago
asked 1 hour ago
asked 2 hours ago