Tensor for Matrix: How to Represent a Given Matrix Using a Tensor

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Homework Help Overview

The discussion revolves around representing a specific matrix using a tensor. The matrix appears to have a pattern involving alternating signs, and participants are exploring how to express its elements in terms of a function.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to define the elements of the matrix, questioning whether the elements are +1 or -1. There is a focus on expressing the matrix elements, aij, as a function of their indices, i and j.

Discussion Status

The discussion is ongoing, with participants seeking clarification on notation and the structure of the matrix. Some guidance has been offered regarding the formulation of aij as a function, but no consensus has been reached on the correct representation.

Contextual Notes

There is uncertainty regarding the specific notation used and the exact nature of the matrix elements. The original poster's attempt at a solution involves a condition based on the sum of indices, which has prompted questions about its clarity and correctness.

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Homework Statement


How can you present the following matrix by a tensor?

+ - + - +...
- + - + - ...
+ - + - +...
.
.
.


The Attempt at a Solution



The sum of indexes where is "=" is even so

+ [aij, i+j = 2n]

How can you write the tensor correctly?
 
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I don't understand any of your notation.

Is the matrix filled with elements that are either +1 or -1 ?

I think you would like to express aij as a function of i and j, right?
 
Phrak said:
Is the matrix filled with elements that are either +1 or -1 ?

I think you would like to express aij as a function of i and j, right?

I am trying to write the +/- rule of the determinant calculation by tensors.
This means that I am trying to get the matrix filled with elements that are either +1 or -1.

2. I feel that the point of tensor analysis is to express aij as a function of i and j.
If this is true, then I would like to express aij as a function of i and j.
 
Ok. You're looking for a function, aij= f(i,j).
 

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