Skalárszorosítása

Skalárszorosítása, also known as scalar multiplication, is a fundamental operation in linear algebra. It involves multiplying a vector by a scalar, which is a real number. The result of this operation is a new vector that has the same direction as the original vector if the scalar is positive, or the opposite direction if the scalar is negative. The magnitude of the new vector is scaled by the absolute value of the scalar.

To perform scalar multiplication, each component of the vector is multiplied by the scalar. For example, if we have a vector v = [v1, v2, v3] and a scalar c, then the scalar multiplication c * v results in a new vector [c*v1, c*v2, c*v3]. This operation is widely used in various fields such as physics, computer graphics, and engineering for transformations, scaling, and interpolation. It is a key concept for understanding more complex vector operations and linear transformations.