Setting Up a Matrix with Order Unity Elements: A Scientist's Guide

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Homework Help Overview

The discussion revolves around setting up a matrix defined by the Gilbert determinant, specifically Hij=(I+j-1)^-1, where the original poster seeks assistance with the matrix's dimensions and setup. The subject area includes linear algebra and determinants.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants express confusion regarding the size of the matrix to be constructed, questioning whether to create matrices of increasing order (1x1, 2x2, 3x3) or a specific size. Others clarify the notation and dimensions involved in the determinant calculation.

Discussion Status

Some participants have provided clarifications about the requirements for the matrix dimensions and the nature of the determinant, while others are still seeking further understanding of the problem's instructions. There is an ongoing exploration of the implications of the order of the matrix.

Contextual Notes

Participants note a lack of explicit direction in the problem statement regarding the setup and computation of the determinant for different orders, leading to questions about the expectations for the assignment.

Ashley1nOnly
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Homework Statement


A determinant with all elements of order unity may be surprisingly small. The Gilbert determinant Hij=(I+j-1)^-1, i,j=2... n is notorious for its small values.

Homework Equations

The Attempt at a Solution


I just need help setting up the matrix and I can solve it myself. Thanks
 
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I know how to find the numbers for the matrix but I'm confused as to how big the matrix is supposed to be. Am I doing a 1 by 1 then a 2 by 2 then a 3 by3 or am I doing a 3 by 3
 
Your notation is a little unclear to me. I assume i represents the matrix row and j represents the matrix column. If that equation is ##H_{ij} = (i+j-1)^{-1}## with dimension equal to 2, then the value of each element is given by this equation with whichever row and column number plugged in.
 
Ashley1nOnly said:
I know how to find the numbers for the matrix but I'm confused as to how big the matrix is supposed to be. Am I doing a 1 by 1 then a 2 by 2 then a 3 by3 or am I doing a 3 by 3

Your problem statement doesn't give any direction for actually solving anything. Is there more to it?
 
Yes sorry. I'm stuck on the part where it says by order of n=1,2, and 3. What is is asking me to do?. I have already found my matrix using the given equation( it repeats itself in a decreasing way)
 
Calculate the value of the Hoover determinant of order n for n=1,2, and 3.

Is the problem
 
If it tells you to solve for an order of 1, 2, and 3, then it's telling you to compute the determinant of a 1x1, 2x2, and 3x3 matrix.
 
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Quick question. When you are finding the determinant of a matrix. Do the rows and columns have to be equal?
 
Ashley1nOnly said:
Quick question. When you are finding the determinant of a matrix. Do the rows and columns have to be equal?

Yes. You can only take the determinant of a square matrix.
 
  • #10
For my answers I got
1
1/12
And I am working on the third
 
  • #11
For the 3 by 3
0.00046297
 
  • #12
That looks right!
 
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