Skalarmultiplikasjon

Skalarmultiplikasjon, also known as scalar multiplication, is a fundamental operation in linear algebra and vector mathematics. It involves multiplying a vector by a scalar, which is a single real number. The result of this operation is a new vector that is scaled by the scalar value. If the scalar is positive, the vector's magnitude increases; if negative, the vector's direction is reversed. Scalar multiplication is denoted by placing the scalar to the left of the vector, as in "k * v", where "k" is the scalar and "v" is the vector.

In two-dimensional space, scalar multiplication affects both the x and y components of a vector. For example, if v = (x, y) and k is a scalar, then k * v = (kx, ky). This operation is crucial in various applications, such as physics, engineering, and computer graphics, where vectors are used to represent quantities like velocity, force, and position.

Scalar multiplication is distinct from vector multiplication, which involves the dot product or cross product of two vectors. It is also different from scalar addition, which involves adding a scalar to each component of a vector. Understanding scalar multiplication is essential for comprehending more complex vector operations and their applications in mathematics and science.