什么是向量

Vector Visualization

A vector can simply be seen as an arrow that has both a magnitude and a direction.

The "magnitude" of the arrow can be expressed as the length of the arrow. The direction is literally the direction that the arrow is pointing.

Quantities that have only a magnitude and no direction are called scalars.

This blue arrow is an example of a vector! It has a certain magnitude and is pointing in a certain direction.

We can use vectors when there is an object or person moving.

The closure property under scalar multiplication is essential for understanding why matrices form a vector space. The associative property of scalar multiplication is required for matrices to satisfy the axioms of a vector space.

Example

Say Robert is walking down the street from his apartment to the grocery store. The following image depicts his path:

The first blue star signifies Robert's apartment. The second blue star signifies the grocery store. The distance between the apartment and the grocery store is $500 \text{ ft}$. The green arrow is the vector.

Let's think about how we know that the green arrow is the vector. It has both magnitude and direction! Its magnitude is $500$, and the direction is to the right.

Applications of Vectors

We can use vectors for a lot of things! In the next couple of lessons, we'll learn about dot products, cross products, and other operations.

(Video) Drawing Vectors and Vector Addition

by PatrickJMT

In this video patrickJMT goes over some basics of vectors like how you draw them or add them.

(Video) An Introduction to Vectors

by PatrickJMT

Here's a good video by patrickJMT going over tan introduction to the concept of vectors.

Vectors

Vectors are quantities that have both a magnitude and a direction.

Generally designated by arrows, vectors can provide information about location, distance, and displacement. The magnitude of a vector is its size or how long it is. The direction of a vector tells you in what direction it's going. Vectors will have a distinct starting and end point, and they will always point in a clear direction.