1. Use
(where
is the 4x4 identity matrix) to show that
a)
with C a constant. Calculate C
b)
with D a constant. Calculate D
c)
1. Use (where is the 4x4 identity matrix) to show that a) with C a constant....
Show that the correlation matrix of any random vector X is nonnegative definite, where the correlation matrix is defined by , (Assume we know that the covariance matrix of X denoted is defined by is nonnegative definite, and . Re IRmxm We were unable to transcribe this imageVar(Xi)Var(X ат ат We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this...
Electrodynamics. Consider a linear medium where and are both zero in the region of interest. Show that the Maxwell's equations are invariant to the transformation where is a dimensionless constant and is a constant but arbitrary angle. In other words, if and are solutions of Maxwell's equations, show that and too. Consider the special case and thus show that, in this sense, the fields and can be interchanged. This property is often named the duality property of the electromagnetic field....
Linear statistical models For ridge regression, we choose parameter estimators b which minimise where is a constant penalty parameter. Show that these estimators are given by 7n i=1 We were unable to transcribe this imageWe were unable to transcribe this image 7n i=1
Let two variables and are bivariately normally distributed with mean vector component and and co-variance matrix shown below: . (a) What is the probability distribution function of joint Gaussian ? (Show it with and ) (b) What is the eigenvalues of co-variance matrix ? (c) Given the condition that the sum of squared values of each eigenvector are equal to 1, what is the eigenvectors of co-variance matrix ? please help with all parts! thank you! X1 We were unable...
COMPLEX ANALYSIS:
Solve the integral
where
and
.
Please use JORDAN'S LEMMA and show all of your work.
Thank you!
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Suppose a
c mod n and bd
mod n.
(a) show that a + b
c + d mod n
(b) show that a * b
c * d mod n.
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1. Find , where s is , . 2. Find , and , lying inside and underneath 3. Find , where in cylinder, and between y=0 and y=1 in the first octant. We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageds 2az - We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageryzds We were unable to transcribe this image ds...
With the standard Dirac Hamiltonian plus Coulomb potential
below:
a) Show that
.
b) Show that
, where
.
c) Show that
.
d) Since
all mutually commute, they should have common eigenfunctions, and
thus using (c), find the eigenvalues of K2 and K, in
terms of j.
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Let X be a banach space such that X= C([a,b]) where - ab+ with the sup
norm. Let x and f X. Show
that the non linear integral equation
u(x) = (sin
u(y) dy + f(x) ) has a solution u X. (the integral is
from a to b).
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Let yp(y) be the C(2) inverse demand function facing a monopoly, where y++ is its rate of output, and let yC(y) be the C(2) total cost function of the monopoly. Assume that p(y)>0, p'(y)<0, and C'(y)>0 for all y++, and that a profit maximizing rate of output exists. Total revenue is therefore given by R(y)=p(y)y. Given that question uses an inverse demand function, the elasticity of demand, namely (y), is defined as (y)= 1/p'y p(y)/y. Why is (y)<0? Prove that...