# Orthogonal Matrices and the dot product

• November 20th 2011, 02:42 PM
tubetess123
Orthogonal Matrices and the dot product
If A is an n x n real matrix, how would I start each part of a proof that A is an orthogonal matrix iff Ax dot Ay = x dot y for all x and y in Rn?
• November 20th 2011, 03:40 PM
Deveno
Re: Orthogonal Matrices and the dot product
start with the fact that $x \cdot y = x^Ty$, where the right-hand side is a matrix product of a 1xn and an nx1 matrix.
• November 20th 2011, 07:18 PM
tubetess123
Re: Orthogonal Matrices and the dot product
Thanks so much! I think I got. I used the fact that A^-1 = A^t iff A is an orthogonal matrix!

Thank you again!