Purchase Solution

Multiplicities and eigenvalues

Not what you're looking for?

Ask Custom Question

Please see the attached Word document.
Thank-you for your help.

Suppose A and B are similar matrices, and that μ is an eigenvalue of A. We know that μ is also an eigenvalue of B, with the same algebraic multiplicity. Suppose that g is the geometric multiplicity of μ, as an eigenvalue of B. Show that μ has geometric multiplicity g as an eigenvalue of A.

Purchase this Solution

Solution Summary

This provides an example of working with geometric multiplicities and eigenvalues.

Solution Preview

Please see the attachment.

Proof:
Since and are similar matrices, then we can find an invertible matrix , such that . Suppose is an eigenvalue of with geometric multiplicity ...

Purchase this Solution


Free BrainMass Quizzes
Graphs and Functions

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

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.

Solving quadratic inequalities

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

Probability Quiz

Some questions on probability