Can Eigenvectors Diagonalize a Matrix with Only One Eigenvalue?

b00tofuu · Dec 14, 2011

Let F= R or C, and A =
[1 2 3] is considered as linear operator in F³
[0 1 2]
[0 0 1]
then the minimal polynomial of A = (x-1)^3, can we say that the primary decomposition thm doesn't give any decomposition, can we find an invertible P s.t P^-1*A*p is a block diagonal matrix?

mathwonk · Dec 18, 2011

it seems 1 is the only eigenvalue. now look for the eigenvectors with that eigenvalue. how many do you find? is that enough to diagonalize the matrix?

Can Eigenvectors Diagonalize a Matrix with Only One Eigenvalue?

Discussion

Undergrad Spinor calculus

Undergrad Matrix representation of rank-2 spinors

Undergrad Looking for a paper about spinors

Undergrad Why are these cycles disjoint and of equal length?

On the Moore–Penrose inverse from a banal linear algebra viewpoint

Undergrad Correct constructed example of Abelian Monoid?

Undergrad Correct state row entries in the following Sequential machine?

Insights Why Vector Spaces Explain The World: A Historical Perspective

Undergrad Quintic Polynomial Tschirnhaus Transform: Possible complex Bring Radicals

Insights Revisiting the Velocity-Time Function

Insights Remote Operated Gate Control System

Insights AI Enriched Problem Solving

Insights Thinking Outside The Box Versus Knowing What’s In The Box

Insights Why Entangled Photon-Polarization Qubits Violate Bell’s Inequality

Insights Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect

Can Eigenvectors Diagonalize a Matrix with Only One Eigenvalue?

Discussion

Similar threads

Undergrad Can one find a matrix that's 'unique' to a collection of eigenvectors?

Undergrad Can Eigenvectors of the Same Eigenvalue Be Orthogonal in a 2x2 Matrix?

Undergrad 2x2 matrix A has only one eigenvalue λ with eigenvector v

Graduate Exponent of matrix/Diagonalization of matrix with repeated eigenvalue

Does there exist a 2x2 non-singular matrix with only one 1d eigenspace?

Graduate How Can a Symmetric Matrix Have 2 Eigenvectors with Only 1 Eigenvalue?

Can a Matrix with Zero Eigenvalue Be Invertible?

Diagonalizing Matrix A: Eigenvalues, Eigenvectors, Matrix P & D

Matrix with One Eigenvalue and Non-Eigenvector Eigenvectors