Introduction

Scalar multiplication is another fundamental operation in the realm of vector algebra. It involves multiplying a vector by a scalar (a real or complex number), affecting the magnitude of the vector without altering its direction.

Applications

Definition and Calculation

If you have a vector A and a scalar c, the scalar multiplication cA is a new vector where each element of A is multiplied by c.

Impact of Scalar Multiplication

Scalar multiplication alters the magnitude of a vector. If the scalar is greater than 1, it results in a vector of greater magnitude, and if the scalar is less than 1 but greater than 0, the resultant vector is of smaller magnitude. A negative scalar flips the vector's direction.

Applications in Various Fields

Scalar multiplication finds broad applications in physics (for scaling force, velocity etc.), computer graphics (scaling objects), and machine learning (weighting inputs).

References

• Scalar Multiplication - Wikipedia
• Scalar Multiplication - Math Insight