Purchase Solution

Linear operators

Not what you're looking for?

Ask Custom Question

Let T be a linear operator on a finite dimensional vector space V. Suppose the minimal polynomial for T is of the form P^n where p is an irreducible polynomial over the scalar field. Show that there is a vector x in V such that the T-annihilator of x is p^n.

Purchase this Solution

Solution Summary

This is a proof regarding linear operators, vectors, and t-annihilators. Irreducible polynomials over the scalar fields are analyzed.

Solution Preview

Please see the attachment.

is a linear operator of a finite dimensional vector space . Assume . The minimal polynomial for is , where is an irreducible polynomial over the scalar field. This means .
For each , we can define the -annihilator as . In your ...

Purchase this Solution


Free BrainMass Quizzes
Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Probability Quiz

Some questions on probability

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.