Matrix S^n: Generalizing Matrix Operations

  • Context: Graduate 
  • Thread starter Thread starter Nusc
  • Start date Start date
  • Tags Tags
    Matrix Operations
Click For Summary
SUMMARY

The discussion centers on the generalization of matrix operations, specifically focusing on the lower triangular matrix S defined in the forum. It is established that for a lower triangular matrix S of size n x n, the operation S^n results in the zero matrix. The participants explore the implications of this property and seek a formal proof for the generalization of S^n for such matrices.

PREREQUISITES
  • Understanding of matrix theory, particularly triangular matrices.
  • Familiarity with matrix exponentiation and its properties.
  • Knowledge of linear algebra concepts such as eigenvalues and eigenvectors.
  • Basic proof techniques in mathematics, especially induction.
NEXT STEPS
  • Study the properties of triangular matrices in linear algebra.
  • Learn about matrix exponentiation and its applications in various fields.
  • Research proof techniques, particularly mathematical induction, for establishing matrix properties.
  • Explore the implications of matrix operations in computational algorithms.
USEFUL FOR

Mathematicians, students of linear algebra, and anyone interested in advanced matrix operations and their theoretical implications.

Nusc
Messages
752
Reaction score
2
If I have a matrix

S =

0 0 0 0 ... 0
1 0 0 0 ... 0
0 1 0 0 ... 0
0 0 1 0 ... 0
...
0 0 0 0 .1.0S^2 =0 0 0 0 ... 0
0 0 0 0 ... 0
1 0 0 0 ... 0
0 1 0 0 ... 0
...
0 0 0 0 1.. 0etc.

going in this way S^n would just be the zero matrix.,
How do I generalize S^n of this matrix?
 
Physics news on Phys.org
If S is a lower triangular matrix (n by n), S^n is the zero matrix.
Now prove.
 

Similar threads

Undergrad Matrix diagonalization algorithm
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad On a bound on the norm of a matrix with a simple pole
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Question from a proof in Axler 2nd Ed, 'Linear Algebra Done Right'
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Calculating the Modal Matrix for A
  • · Replies 9 ·
Replies
9
Views
4K
Undergrad Dfns group action & group, written in terms of the other
  • · Replies 26 ·
Replies
26
Views
2K
Undergrad Row space, Column space, Null space & Left null space
  • · Replies 8 ·
Replies
8
Views
3K
MHB Diagonalizable transformation - Existence of basis
  • · Replies 52 ·
2
Replies
52
Views
4K
Undergrad How can I convince myself that I can find the inverse of this matrix?
  • · Replies 34 ·
2
Replies
34
Views
3K
Undergrad Dimension of a Linear Transformation Matrix
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Solving matrix commutator equations?
  • · Replies 7 ·
Replies
7
Views
4K