What is the purpose of this matrix operator?

  • Thread starter Thread starter operationsres
  • Start date Start date
  • Tags Tags
    Matrix Operator
operationsres
Messages
99
Reaction score
0
Hi,

w1e7w2.png

A fuller view can be found here:
4q56c0.png


(i) What is this operator?
(ii) What does this operator mean if Sp is a 5x5 matrix and (Z'Z)-1 is a 3x3 matrix?Thanks a lot.
 
Last edited:
Physics news on Phys.org
Hey operationsres.

Can you give the context for this notation? Where did you see it? A book? A website? Are you taking a class on something?
 
(1) This is from an econometrics paper "An Approach to Statistical Inference in Cross-Sectional Models with Security Abnormal Returns As Dependent Variable" published in 1986.

(2) Here's the context of the equation:
http://i49.tinypic.com/4q56c0.png

Note that Sp is necessarily a square matrix, as is (Z'Z)^-1 however they are different dimensions...
 
Oh awesome if you're right. Kind of like A x B where A and B are sets!

:)
 
operationsres said:
Oh awesome if you're right. Kind of like A x B where A and B are sets!

:)

I'd check though in the context of the linear models for the GLAM stuff because that will give you context not just for the equations (and if the operator is that) but also for what it's actually doing which is going to be more important.
 
Thread 'Determine whether ##125## is a unit in ##\mathbb{Z_471}##'
This is the question, I understand the concept, in ##\mathbb{Z_n}## an element is a is a unit if and only if gcd( a,n) =1. My understanding of backwards substitution, ... i have using Euclidean algorithm, ##471 = 3⋅121 + 108## ##121 = 1⋅108 + 13## ##108 =8⋅13+4## ##13=3⋅4+1## ##4=4⋅1+0## using back-substitution, ##1=13-3⋅4## ##=(121-1⋅108)-3(108-8⋅13)## ... ##= 121-(471-3⋅121)-3⋅471+9⋅121+24⋅121-24(471-3⋅121## ##=121-471+3⋅121-3⋅471+9⋅121+24⋅121-24⋅471+72⋅121##...
It is well known that a vector space always admits an algebraic (Hamel) basis. This is a theorem that follows from Zorn's lemma based on the Axiom of Choice (AC). Now consider any specific instance of vector space. Since the AC axiom may or may not be included in the underlying set theory, might there be examples of vector spaces in which an Hamel basis actually doesn't exist ?
##\textbf{Exercise 10}:## I came across the following solution online: Questions: 1. When the author states in "that ring (not sure if he is referring to ##R## or ##R/\mathfrak{p}##, but I am guessing the later) ##x_n x_{n+1}=0## for all odd $n$ and ##x_{n+1}## is invertible, so that ##x_n=0##" 2. How does ##x_nx_{n+1}=0## implies that ##x_{n+1}## is invertible and ##x_n=0##. I mean if the quotient ring ##R/\mathfrak{p}## is an integral domain, and ##x_{n+1}## is invertible then...
Back
Top