skalárszorzást

Skalárszorzás is the Hungarian term for scalar multiplication. In mathematics, scalar multiplication is an operation that takes a scalar (a number) and a vector as input and produces a vector as output. The scalar acts as a multiplier for each component of the vector. For example, if we have a scalar k and a vector v = [v1, v2, ..., vn], then the scalar multiplication k * v results in a new vector [k*v1, k*v2, ..., k*vn].

The scalar multiplier determines the scaling of the vector. If the scalar is greater than 1, the vector is stretched. If the scalar is between 0 and 1, the vector is compressed. If the scalar is negative, the vector is reversed in direction and scaled. If the scalar is 0, the result is the zero vector.

Scalar multiplication is a fundamental operation in linear algebra and has numerous applications in physics, computer graphics, and engineering. It is a key component in defining vector spaces and understanding linear transformations. For instance, in physics, scalar multiplication can represent changes in magnitude or intensity of a physical quantity represented by a vector. In computer graphics, it's used for scaling objects in 2D or 3D space. The properties of scalar multiplication, such as distributivity over vector addition and associativity with scalar addition, are crucial for algebraic manipulations involving vectors.