Sorry about that. Its more than obvious that it is impossible to solve the problem as I stated it before.
Let me give you some more information about my issue. And what I want to do. Perhaps that will make it more clear.
Suppose we have a wig with a centre of gravity x and a rotating point o...
Hey,
I have a problem that can be written in the following form:
u=v x w
where u, v, w are 3by1 vectors and x is the cross product.
now I want to write v in term of u and w, but I have no idea of how to get vector v out of the previous equation. Someone who can help me with this...
For a kinematic problem I obtained the following equations:
p1=- r*sin(theta_c) - d*cos(psi_a)*sin(theta_a)+c1
p2=d*sin(psi_a)*sin(theta_a)+c2
p3=d*cos(theta_a) + r*cos(theta_c)+c3
I want to solve these equations for theta_a, psi_a, theta_c, assuming that all other variables are known...
Suppose we've got the setup as shown in the figure (see attachment).
The idea is that the motor transfers its speed and force (rotary) to the actuator force and speed (linear) via some gears and a spindle.
Here:
R = radius [m]
J = inertia [kg m^2]
n = rotary to linear transmission [---]...
So if I understand it correctly I can say that
\lambda_{\max} (A) + \lambda_{\max} (B) \geq \lambda_{\max} (A+B)
can be written as
\max_{||x_{1}||=1} x_{1}^*Ax_{1} + \max_{||x_{2}||=1} x_{2}^*Ax_{2} \geq \max_{||x_{3}||=1} (x_{3}^*Ax_{3} + x_{3}^*Bx_{3})
The terms on the left hand side...
But if you state it this way, then it seems to me that the inequality holds with equality...
For example, if
S1 = {1,2}
S2 = {2,3}
then the set of sums S12 = s1+s2 is equal to
S12 = {3,4,5}
So if we consider max(S12) and max(S1)+max(S2), then aren't those equal to each other?
Homework Statement
Proof: \lambda_{\max}(A+B) \leq \lambda_{\max}(A) + \lambda_{\max}(B)
Homework Equations
Hint from exercise: \lambda_{\max}(A)=\max_{\|x\|=1} x^*Ax
The Attempt at a Solution
The problem is that the equation on the left side can not be split. So I tried to...
Found partly what I needed:
\lambda_{\max}(A)I \geq A \geq \lambda_{\min}(A)I
\beta I > A \iff \beta > \lambda_{\max}(A)
Now all I have to know is what is known for the eigenvalue of two matrices? That is:
\lambda_{\max}(A+B) = ...
Is there any expression I can use for such an...
Ok, but I think this holds true:
Suppose A-B is hermitian and positive definite, then
\max_{\|x\|=1} x^*(A-B)x \geq x^*(A-B) x = x^*Ax - x^*Bx \leq \lambda_{\max}(A) - \lambda_{\max}(B)
Sorry I went to fast here. With the maximum I meant the largest (or maximal) eigenvalue, for example
\lambda_{\max}(A) = \max_{\| x \| =1} x^* A x
Then my question is: what do I know of this operator? Is it, eg, linear?
Does anybody have a good book/website where I can find good information on how to use the maximum on matrices. I have to prove an expression involving the maximum and eigenvalue of matrices. But I don't know how to link those to together. I think I can figure this out, if only I had some good...
yes that is right, the limit does not exist. I misused this term. Indeed I am looking for a value for f(i0,z0) such that the function is continuous at this point.