refleksjonsmatrise

A refleksjonsmatrise, or reflection matrix in English, is a mathematical tool used in linear algebra to represent a geometric reflection. It is a square matrix that, when multiplied by a vector, transforms that vector into its reflection across a specific line or plane. The dimensions of the matrix correspond to the dimensions of the space in which the reflection occurs. For example, a 2x2 matrix can represent a reflection in a 2D plane, while a 3x3 matrix is used for reflections in 3D space.

The specific entries of a refleksjonsmatrise are determined by the orientation of the line or plane of reflection. For a reflection across a line in 2D, the matrix will typically have entries related to the cosine and sine of the angle the line makes with an axis. In 3D, the process is similar but involves more complex calculations based on the normal vector to the plane of reflection.

Applying a refleksjonsmatrise to a point or vector effectively flips it to the other side of the reflection line or plane while preserving its distance from that line or plane. This operation is common in computer graphics for creating mirrored images, in physics for simulating symmetrical phenomena, and in various areas of engineering and geometry for transformations. The inverse of a reflection matrix is the matrix itself, meaning that reflecting twice across the same line or plane returns the original vector.