Generalized eigenspace invariant?

Click For Summary
The discussion centers on whether the generalized eigenspace is invariant under a finite-dimensional linear operator T on complex numbers. The generalized eigenspace for an eigenvalue y is defined as the set of vectors v in V such that there exists a j≥1 where (T - yI)^j(v) = 0. Participants seek clarification on the meaning of "invariant" in this context and request a proof of the invariance property. The conversation emphasizes the need for a deeper understanding of these mathematical concepts. Overall, the inquiry aims to establish the relationship between generalized eigenspaces and linear operators.
mind0nmath
Messages
19
Reaction score
0
Hey,
Is the generalized eigenspace invariant under the operator T? Let T be finite dimensional Linear operator on C(complex numbers).
My understanding of the Generalized Eigenspace for the eigenvalue y is:
"All v in V such that there exists a j>=1, (T-yIdenitity)^j (v) = 0." plus 0.
thanks
 
Physics news on Phys.org
What does invariant mean? Try to prove it.
 
got it. thanks.
 

Thread 'Confusion about the Moyal-Weyl twist'

I am studying the mathematical formalism behind non-commutative geometry approach to quantum gravity. I was reading about Hopf algebras and their Drinfeld twist with a specific example of the Moyal-Weyl twist defined as F=exp(-iλ/2θ^(μν)∂_μ⊗∂_ν) where λ is a constant parametar and θ antisymmetric constant tensor. {∂_μ} is the basis of the tangent vector space over the underlying spacetime Now, from my understanding the enveloping algebra which appears in the definition of the Hopf algebra...
View full post »

Similar threads

Undergrad If T is diagonalizable then is restriction operator diagonalizable?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Proof by induction of block diagonal decomposition of a matrix
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Orthogonality of Eigenvectors of Linear Operator and its Adjoint
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad General Linear Group GL(n) on Vector Spaces and canonical pairing invariance
  • · Replies 1 ·
Replies
1
Views
3K
Generalised eigenspace contains the eigenspace?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Question from a proof in Axler 2nd Ed, 'Linear Algebra Done Right'
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Confused about small detail in rank-nullity theorem
  • · Replies 1 ·
Replies
1
Views
2K
High School Higher Dimensional Vectors
  • · Replies 5 ·
Replies
5
Views
1K
Undergrad Question about an eigenvalue problem: range space
  • · Replies 1 ·
Replies
1
Views
2K
MHB Is the Matrix A Diagonalizable with Real Eigenvalues?
  • · Replies 10 ·
Replies
10
Views
2K