Introduction

Vector subtraction is a fundamental operation in the field of linear algebra and has wide applications in physics, computer graphics, and machine learning. This operation is performed element-wise between two vectors of the same dimension.

Applications

Definition and Calculation

Let's consider two vectors A and B of the same dimension, n. The subtraction of B from A, denoted as A - B, results in another vector, where each element is the difference between the corresponding elements in A and B.

Uses of Vector Subtraction

Vector subtraction is often used in physics to calculate displacement, in computer graphics for manipulations and transformations, and in machine learning algorithms to compute error or difference vectors.

Visualizing Vector Subtraction

In a Cartesian coordinate system, vectors can be visualized as arrows pointing from the origin to the point represented by the vector. Vector subtraction can then be visualized geometrically as the process of "reversing" the second vector and adding it to the first vector.

References

• Euclidean Vector - Wikipedia
• Vector Subtraction - Math Insight