# Math Help - Orthogonal Matrices

1. ## Orthogonal Matrices

A and B are orthogonal.

Where H is the Householder transformation. According to the book, the result should be -b, not b. I reasoned since a and b were orthogonal that a^t b =0. It is true that H_a a =-a. Any ideas?

2. ## Re: Orthogonal Matrices

Hey Hal2001.

If a and b are orthogonal then I agree that the whole right term should disappear since matrix multiplication is associative so you can calculate (2/c*a)*(a^t*b) = blah * 0 = 0.

But why are you assuming a is orthogonal to b? Is that assumed in your work or by your teacher?

3. ## Re: Orthogonal Matrices

Hello,

The book gives a is orthogonal to b.

4. ## Re: Orthogonal Matrices

Well what you did looks right: I can't really fault what you've done if a^t*b = 0 and all the operations are associative which they are if they are matrices.

5. ## Re: Orthogonal Matrices

Okay thanks. Probably just a typo.