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And summation?
Given the following function
Given that all the eigenvalues of I-B, where I is the identity matrix, satisfy
OK, I reduced the problem to the following: Suppose a square matrix A is given, with D being a diagonal matrix containing only its diagonal entries
which are positive.
It is known that the eigenvalues of
The function is f(x), resulting in a value, it is clear that
x_0, x_1, and b are column vectors, and their transposes are row vectors.
(vectors are oriented to allow the operations)
Sorry, I thought the notation would suffice.
x and b are vectors;
A, R, D are matrices;
as for the second question: suppose a square matrix A is given.
Now split A = D + R, such that D is a square diagonal matrix with diagonal entries of A
(hence, the matrix R entries would be the off-diagonal entries of A)
I'm trying to resolve the following:
given a function
I apologize for not making it precise.
All the elements
Suppose the following relation holds
Suppose matrices C \in R^{nxk} and X \in R^{nxk} are given, and it is known that X minimizes the expression
Recently I was assigned to implement a procedure involving "3D projections" to "2D space". Supposing that 3D data is stored in a n x 3 matrix X, the final step involves Y=XP, where P is a 3x2 matrix. However, I would need to be sure about the actual meaning of the word "projection" to 2D. In my understanding (I deliberately tend to be descriptive), there are some points in 3D, I'm looking at it from above, and there is a piece of paper below the data (paper is fixed).
So, each time I multiply XP to obtain Y in 2D, it actually means I'm changing the viewpoint, and Y actually corresponds to what I see when looking at the data (as on the fixed paper), right? In other words, with every P, I'm changing the viewpoint and taking the picture (or drawing on a paper, thus 2D) of what I see? If so, that would mean that for any P there is a viewpoint. Please correct me if I'm wrong.
Suppose you're given a function
Any suggestions on how to proceed?
Thanks
The relation is guaranteed to work for p=[0, 1]. However, I'm faced with certain extensions. Namely,
given
I know that for p>1 it does not work. But I wonder if it works for p from the interval [0, 1], meaning any number between 0 and 1; 0.5 for example.
An example where it does not work for this p?
Thanks for the message.
I would appreciate if you could share the reasons.
Under the assumption
, I'm trying to obtain values of p such that .Thanks
Unfortunately, the values of a_i and b_i are different.
Would the expression depend on the largest a_i and b_i dominantly (meaning, the final min value of f(t) mostly depend on some specific a_i and b_i, compared to other a_i and b_i values)?
The function would then look like:
What would now be the value of t for min f(t)? I guess this simplifies the matter
Thanks.
But, how do you account for the summation? Also, you're introducing the exponent term in the solution again.
The question is to find t for which f(t) is minimum.
Given a certain function f(x), the value of x for which f(x) is minimum is found through differentiation.
Suppose a function
The condition
The following is an approximation problem. Given a ratio:
I wonder what steps to follow to give a reasonable approximation.
This is an intuition
Also, as for the conditions, I thought of
I guess the solution is the weighted average. Or?
Thanks a lot. I tried to extend the procedure by incorporating the effect of a function f(x)=x^p.
So, I'm trying to incorporate it for individual terms.
Then, extracting the a, b, c terms is not so easy. Perhaps I would need to take different approach.
Thanks.
Thanks. What would be the relation of D1 and D2 values associated with sets G1 and G2: G1 and G2 having the same length and same standard deviation?
In other words, given two sets G1 and G2 of equal length, what condition needs be satisfied for D1=D2; they would need to have same standard deviation, or same mean?