skalárszorosán

skalárszorosán is a Hungarian term that translates to "scalar multiplication" in English. It refers to the operation of multiplying a vector by a scalar quantity. This operation is fundamental in linear algebra and has applications in various fields of mathematics, physics, and engineering.

When a vector is multiplied by a scalar, the result is a new vector that has the same direction as the original vector but a different magnitude. If the scalar is positive, the new vector points in the same direction. If the scalar is negative, the new vector points in the opposite direction. If the scalar is zero, the resulting vector is the zero vector, which has zero magnitude and no defined direction.

Mathematically, if v is a vector and c is a scalar, then the scalar multiplication of v by c is denoted as cv. If v is represented by its components (v1, v2, ..., vn), then cv is calculated by multiplying each component of v by c: cv = (cv1, cv2, ..., cvn).

The properties of scalar multiplication include distributivity over vector addition (c(u + v) = cu + cv), associativity with scalar multiplication (a(bv) = (ab)v), and the identity property for the scalar 1 (1v = v). These properties are crucial for manipulating vector equations and understanding vector spaces. Scalar multiplication is a key concept that underpins many advanced mathematical and scientific theories.