Finding Jordan forms over the complex numbers

chuckles1176 · Dec 14, 2009

So I am trying to compute all possible Jordan forms over the complex numbers given a minimal polynomial. My question is this: If the roots of the minimal polynomial are both real, should I proceed as if all of the possible forms are over real numbers?

HallsofIvy · Dec 15, 2009

The Jordan forms are always matrices with the eigenvalues on the diagonal and either "0" or "1" (in some notations, below) above each eigenvalue. If all the eigenvalues are real, I can see no way to introduce complex numbers into them.

Spartan Math · Dec 19, 2009

chuckles, do you by any chance go to Michigan State?

Finding Jordan forms over the complex numbers

Thread 'The colorful world of ##2\times 2## complex matrices'

Thread 'When are Markov Matrices also Martingales?'

Similar threads

Hot Threads

I How to show ##p(x)=g(x)x\pm 1\in\Bbb{Q}[x]## is irreducible in ##\Bbb{Q}_{\Bbb{Z}}[x]##?

I Showing ##k[x_1,\ldots,x_n]/\mathfrak{a}## is finite dimensional

I How do we distinguish two different notations for cokernel and coimage?

I Localising a non integral domain at a prime

I ##(A/\mathfrak{a})_{\mathfrak{p}/\mathfrak{a}}## and its isomorphism?

Recent Insights

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

Insights What Exactly is Dirac’s Delta Function? - Insight

Insights Relativator (Circular Slide-Rule): Simulated with Desmos - Insight

Insights Fixing Things Which Can Go Wrong With Complex Numbers