Linear models is the topic
And i believe my professor wrote this n*Sum(XiYi) - Sum(XiYi) = Sum(Xi - Xbar)(Yi - Ybar)
i was hoping if some one could tell me if this is true of if it is my bad in typing down.
If it is true then can some one please tell me how?
I've attached an image...
My professor sucks
she hasnt gone over mean vector and she expects up to solve this
let z1, z2, z3 be the random variables with mean vector and covariance matrix given below
mean vector = [1 2 3]T. T = transpose
covariance vector
3 2 1
2 2 1
1 1 1
Define the new variables...
I need to know if there is any relationship between the positive definite matrices and its eigenvalues
Also i would appreciate it if some one would also include the relationship between the negative definite matrices and their eigenvalues
Also can some also menthow the Gaussian...
Yeah that is the complete problem statement.
but it is a question from my Optimization class and not Linear Algebra
I don't understand how the zero matrix will fit the bill
So i have a problem in front of me
Let A be a m x n matrix whose rows are linearly independent. Prove that there exists a vector p such taht Ap = e_1 where e_1 =( 1, 0 , 0, 0, 0,0 ,0 ... 0)T
i don't even know where to begin
So i need to show if a matrix is positive definite or negative or neither
I have a matrix 3x3 A so i compute xTAx
I am left with an quadratic equation interms of x_1 x_2 and x_3
The Matrix is of the form
A = [ 9 -1 2]
|-1 7 -3|
[2 -3 3]
and solving xTAx i get...
Hey So i need to write down the first order necessary condition (F.O.C). and i need to find out where does a stationary point exist
I know how to solve for the F.O.C when i am given an equation in the standard quadratic polynomial form but here the equation is
f(x) = 1/2 xT Qx - cTx
where T...
Homework Statement
Prove that the intersection of a number of finite convex sets is also a convex set
Homework Equations
I have a set is convex if there exists x, y in the convex S then
f(ax + (1-a)y< af(x) + (1-a)y
where 0<a<1The Attempt at a Solution
i can prove that
f(ax + (1-a)y) <...
i need a decent book for linear and non linear optimization.
Currently i am using Linear and Non linear optimization by Griva Nash and Sofer, and it is by far the worst math book i have ever used. It does not have any solved examples or anything. It does not even have any proofs. It has...
This is exactly how the problem goes
let f(x) be a function in Rn.
prove that f(x) is both concave and convex if f(x) = cTx for some vector c
I thought that the function was a affine function, but i can't prove it
Ok, i am seriously lost, i don't know where to bring in z from..
I am attaching the only pages where convex sets have been defined and from the material, and with the information given, it seems difficult to prove the above
Homework Statement
In my textbook, the author briefly makes a statement that affine functions are both concave and convex, how is that true? and how can it be proven?
Homework Equations
The Attempt at a Solution