Question

How do you check if a transformation is orthogonal?

Answer 1

if you take integral of product of original and tranformation you get zero.

Not sure , just thinking

Answer 2

To check, you can take the cross product, this should allow you to solve for the angle, which will tell you if it is indeed orthogonal

Answer 3

If A is orthogonal

columns/rows of A form an orthonormal basis
A^TA = In
A^-1 = A^T
<v,w> = <Av,Aw>

Answer 4

I have this thing where it says like T:R^2 --> R^2 is an orthogonal linear operator then the standard matrix is orthogonal

Answer 5

by definition

Answer 6

so would I just find the standard matrix I don't get the difference between

Answer 7

transformation and matrix

Answer 8

b/c on my sheet it says know how to check if a transformation or matrix is orthogonal

Answer 9

I know how to check a matrix A^-1 = A^T

Answer 10

If a matrix A represents an orthogonal transformation then A is an orthogonal matrix.

Answer 11

columns/rows of A form an orthonormal basis

is usually the easiest check...

Answer 12

Okay thanks! Make sense