Finding the Order of a 2x2 Matrix

  • Thread starter Thread starter ns5032
  • Start date Start date
  • Tags Tags
    Matrix
Click For Summary
SUMMARY

The discussion focuses on determining the order of a 2x2 matrix in the context of linear transformations. The order of a matrix is defined as the smallest integer n such that raising the matrix to the n-th power results in the identity matrix. In this case, the transformation represented by the 2x2 matrix has an order of 3, meaning that the third power of the matrix equals the identity matrix while the second power does not.

PREREQUISITES
  • Understanding of linear transformations
  • Knowledge of matrix exponentiation
  • Familiarity with the identity matrix
  • Basic concepts of matrix algebra
NEXT STEPS
  • Learn about matrix exponentiation techniques
  • Study the properties of the identity matrix
  • Explore linear transformations and their applications
  • Investigate higher-order matrices and their characteristics
USEFUL FOR

Students and professionals in mathematics, particularly those studying linear algebra, as well as anyone involved in computational mathematics or engineering applications requiring matrix analysis.

ns5032
Messages
27
Reaction score
0
I have a specific 2 by 2 matrix, but obviously I don't want the answer to my actual problem, so can someone just explain to me the general process of finding the order of a 2x2 matrix??
 
Physics news on Phys.org
What is the definition of "order of a matrix"?
 
You know as well as I do. The problem I am given states:

"Given a linear transformation given by the matrix equation:

(x',y') = (x,y) (a specific 2x2 matrix with some number b included, which I will leave out for now),

show that this transformation has order 3, no matter what b is."
 
No, I don't know what definition you are using for "order of a matrix" which is what you asked. The only definition I know would say that the order of a 2 x 2 matrix is "2 x 2".

There is, however, an "order" of a LINEAR TRANSFORMATION which you now mention. It is the smallest power, n, such that Tn is the identity. If that is the definition you are using just calculate the square and third power of your matrix. If the square is not the identity but the third power is, then the linear transformation has "order" 3.
 

Similar threads

How to find the determinant of this matrix?
  • · Replies 3 ·
Replies
3
Views
1K
Linear operator in 2x2 complex vector space
  • · Replies 18 ·
Replies
18
Views
3K
Linear Algebra Determinant proof
  • · Replies 4 ·
Replies
4
Views
1K
Does there exist a 2x2 non-singular matrix with only one 1d eigenspace?
  • · Replies 2 ·
Replies
2
Views
2K
Is this vector in the image of the matrix?
  • · Replies 4 ·
Replies
4
Views
3K
Fundamental matrix for complex linear DE system
  • · Replies 4 ·
Replies
4
Views
1K
Is the Cube of matrix associative?
  • · Replies 3 ·
Replies
3
Views
2K
Find a 2x2 Matrix with given EigenValues
  • · Replies 5 ·
Replies
5
Views
7K
Undergrad Is a 1x1 Matrix Considered a Scalar in Mathematics?
  • · Replies 12 ·
Replies
12
Views
3K
Construct a 2x2 matrix that expresses a given transformation
  • · Replies 5 ·
Replies
5
Views
2K