Eigenvectors and eigenvalues
Not what you're looking for?
Please see the attached Word document.
Thank-you very much for your help.
Suppose that A and B are n x n matrices such that A = SBS-1 (where S is an invertible matrix), so A and B are similar matrices.
(a) Show: if v is an eigenvector of B with eigenvalue μ, then Sv is an eigenvector for A.
(Remember that only nonzero vectors can be eigenvectors.)
What is the corresponding eigenvalue?
(b) Suppose that w is an eigenvector of A with eigenvalue β. Find an eigenvector for B which has the same eigenvalue β.
Purchase this Solution
Solution Summary
This provides examples of working with eigenvectors and eigenvalues of matrices.
Solution Preview
Please see the attachment.
Proof:
(a) If is an eigenvector of with eigenvalue , ...
Purchase this Solution
Free BrainMass Quizzes
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.
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.
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts