Purchase Solution

orthogonal matrix

Not what you're looking for?

Ask Custom Question

How can I show that O(n) and SO(n) x Z2 are homeomorphic? O(n) is the orthogonal group and SO(n) is the special orthogonal group.

Purchase this Solution

Solution Summary

The determinant of an orthogonal matrix is provided.

Solution Preview

The determinant of an orthogonal matrix is either 1 or (-1). It's very easy to see. Since if A belongs to O(n), then we have A^T A = I, and
det(A) = det(A^T), taking the determinants of both sides of the equation A^T A = I, we get (det(A))^2 = 1, so det(A) = 1 or det(A) = -1.
The determinant of a matrix B from SO(n) ...

Purchase this Solution


Free BrainMass Quizzes
Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Solving quadratic inequalities

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

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.

Graphs and Functions

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