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Hi there,

I am have trouble with a proof. I have some steps done, but I am not sure if I am aproaching this correctly.

the question is:

Show that the matrix of any reflection in R^n is a symmetric matrix.

I know that F(x) = Ax + b is an isometry

where A is an Orthoganol matrix , and vector b is in R^n

this implies that A^t A = I (identity matrix) iff A^-1 = A^t

and if f is a reflection then f(f(x)) = x

then f(f(x)) = A(Ax + b) + b = x

_________

i need to somehow prove that A = A^t which then means the matrix is symmetric

thank you for you time and help

regards,

adam

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# Homework Help: Geometry help

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