Purchase Solution

Linear Algebra - Linear Functionals

Not what you're looking for?

Ask Custom Question

See the attached file.
Now let V be the space of all 2x2 matrices over the field F and let P be a fixed 2x2 matrix. Let T be the linear operator on V defined by T(A) =PA. Prove that tr(T)=2tr(P).

From a previous exercise we know that similar matrices have the same trace. Thus we can define the trace of a linear operator on a finite-dimensional space to be the trace of any matrix, which represents the operator in an ordered basis. This is well defined since all such representing matrices for one operator are similar.

Attachments
Purchase this Solution

Solution Summary

Linear functionals are investigated. The solution is detailed and well presented.

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

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

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.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.