Reflections calculator

This page provides two calculators related to calculating reflections in a the real Euclidean vector space $\mathbb{R}^n$ with the standard inner product

The reflection

This calculator computes $s_\alpha(v)$ , the reflection of a vector $v$ through the hyperplane perpendicular to $\alpha$ .

Input

Enter the vector

\alpha

as a comma seperated list with parenthesis, e.g:

(-3, 0, 1, 4.5)

Enter the vector

v

as above:

Result

Your answer will display here.

Vectors generated by reflections

The calculator below allows you to enter a list of vectors $v_1, v_2,\ldots,v_p$ and will return a list of vectors that is the result of applying $s_{v_i}(v_j)$ for every pair of vectors.

Input

Put your input in the box below, formatting vectors as above and separating each vector with a line break like this:

          (-3, 0, 1, 4.5)
          (1, 0, -1, 2)
          (1.5, 1, 0, 0)

Result

Your answer will display here.