Scalar multiplication is a mathematical operation that involves multiplying a vector by a scalar, which is a single number. This operation scales the vector's magnitude without changing its direction. For example, if you have a vector v and a scalar k, the result of the multiplication k * v will produce a new vector that is k times longer or shorter than v. In a geometric sense, scalar multiplication can be visualized as stretching or compressing the vector. If the scalar is greater than 1, the vector is stretched; if it is between 0 and 1, the vector is compressed. If the scalar is negative, the vector is also reversed in direction. This concept is fundamental in linear algebra and is widely used in various fields, including physics and computer graphics.