Purchase Solution

Matrix Theory - Isometries

Not what you're looking for?

Ask Custom Question

Find the eigenvalues and eigenvectors of A.
See attached file for full problem description.

Consider the matrices in O(2) of the form:


these matrices correspond to the elements of O(2) with det(A)= -1. Find the eigenvalues and eigenvectors of A.

Purchase this Solution

Solution Summary

This shows how to find eigenvalues and eigenvectors.

Solution Preview

I will use t instead of theta, it is easier to write; to find the eigenvalues we need to solve Det(A-xI)=0, which means:
(cost-x)(-cost-x)-sint*sint=0 so:
x^2=1 (using that the cos^2+sin^2=1).
So x1=1 and x2=-1 are the eigenvalues.
In what follows we will assume sint non-zero. If sint is zero, we discuss in the end of the proof what the answer is.
Eigenvectors for ...

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.

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.

Probability Quiz

Some questions on probability

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Multiplying Complex Numbers

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