What would be the best word to describe this behavior?

  • Thread starter Thread starter TheMathNoob
  • Start date Start date
  • Tags Tags
    Behavior
AI Thread Summary
The matrices presented are related through their structure, with non-zero entries positioned in a consistent anti-diagonal pattern. They can be described as anti-diagonal matrices, which are characterized by having non-zero elements only on the anti-diagonal. Additionally, the matrices can be expressed as linear combinations of vectors, with the first matrix representing a simple reflection. The other matrices exhibit similar properties but include scaling transformations in the x and y directions. This relationship is useful for the mathematical proof being developed.
TheMathNoob
Messages
189
Reaction score
4

Homework Statement


I have the following matrices
0 1
1 0

0 2
3 0

0 8
7 0
As you can see, the only thing that changes in the matrices are their non-zero entries. How can you relate those matrices by using a simple word or definition?. I need it for a mathematical proof that I am doing.

Homework Equations

The Attempt at a Solution

 
Physics news on Phys.org
TheMathNoob said:

Homework Statement


I have the following matrices
0 1
1 0

0 2
3 0

0 8
7 0
As you can see, the only thing that changes in the matrices are their non-zero entries. How can you relate those matrices by using a simple word or definition?. I need it for a mathematical proof that I am doing.

Homework Equations

The Attempt at a Solution

Have you tried looking at how you'd write them as a linear combination of the vectors? You can relate all three by weighting the vectors..
 
The first one is a simple reflection. The others idem but 'followed' by a stretch in x and y directions
 

Thread 'Finding the number of ways to arrange identical balls in a circle (3 different colors)'

I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
View full post »

Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
View full post »

Similar threads

Prove the identity matrix is unique
2
Replies
69
Views
8K
A gardener collected 17 apples...
Replies
32
Views
2K
How Do Hadamard Matrices Relate to Identity Matrices?
Replies
2
Views
2K
Given specific v, dimension of subspace of L(V, W) where Tv=0?
Replies
15
Views
2K
Proof via mathematical induction
Replies
17
Views
2K
A Gamma matrices and Gell-Mann's I - Y categorization
Replies
22
Views
2K
Induction Proof for 2^n x 2^n Matrix Using L Transformation
Replies
4
Views
2K
Finding Matrices E & F: A Matrix Challenge
Replies
5
Views
2K
I On a bound on the norm of a matrix with a simple pole
Replies
8
Views
3K
Prove true or false eigenvalue question
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top