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

  • Thread starter Ashley1nOnly
  • Start date
  • Tags
    Matrix Set
In summary, the Gilbert determinant Hij=(I+j-1)^-1, i,j=2...n is known for its small values and can be calculated for different matrix orders, such as 1x1, 2x2, and 3x3. The determinant of a matrix can only be taken for a square matrix, where the number of rows and columns are equal. The values for the determinant for orders 1, 2, and 3 are 1, 1/12, and 0.00046297 respectively.
  • #1
Ashley1nOnly
132
3

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
 
Physics news on Phys.org
  • #2
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
 
  • #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.
 
  • #4
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?
 
  • #5
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)
 
  • #6
Calculate the value of the Hoover determinant of order n for n=1,2, and 3.

Is the problem
 
  • #7
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.
 
  • Like
Likes Ashley1nOnly
  • #8
Quick question. When you are finding the determinant of a matrix. Do the rows and columns have to be equal?
 
  • #9
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!
 
  • Like
Likes Ashley1nOnly

1. How do I create a matrix?

To create a matrix, you will need to first determine the size of your matrix (number of rows and columns). Then, you can either manually enter the values into the matrix or use a programming language to generate the matrix.

2. What is the purpose of a matrix?

A matrix is a mathematical tool used to organize and manipulate data. It is commonly used in fields such as statistics, computer science, and engineering to perform calculations and solve problems.

3. How do I add or subtract matrices?

To add or subtract matrices, they must have the same dimensions. Then, you can simply add or subtract the corresponding elements in each matrix to create a new matrix with the same dimensions.

4. Can I multiply any two matrices?

No, matrix multiplication is only defined for matrices with compatible dimensions. The number of columns in the first matrix must match the number of rows in the second matrix in order to multiply them.

5. How do I set up a matrix for solving a system of equations?

To set up a matrix for solving a system of equations, you will need to write the coefficients of each variable as the elements of the matrix, with the constants on the right side. Then, you can use matrix operations to solve the system of equations.

Similar threads

  • Calculus and Beyond Homework Help
Replies
1
Views
986
  • Calculus and Beyond Homework Help
Replies
5
Views
10K
  • Calculus and Beyond Homework Help
Replies
3
Views
1K
  • Calculus and Beyond Homework Help
Replies
6
Views
2K
  • Calculus and Beyond Homework Help
Replies
3
Views
1K
  • Calculus and Beyond Homework Help
Replies
2
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
7
Views
1K
  • Calculus and Beyond Homework Help
Replies
1
Views
2K
  • Calculus and Beyond Homework Help
Replies
3
Views
2K
  • Calculus and Beyond Homework Help
Replies
5
Views
961
Back
Top