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?

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- Nov 20th 2011, 01:42 PMtubetess123Orthogonal 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?

- Nov 20th 2011, 02:40 PMDevenoRe: Orthogonal Matrices and the dot product
start with the fact that $\displaystyle x \cdot y = x^Ty$, where the right-hand side is a matrix product of a 1xn and an nx1 matrix.

- Nov 20th 2011, 06:18 PMtubetess123Re: 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!