Essence of linear algebra

[[Reading Status Button]]

Physics: A Vector is defined by its length and direction. As long as it is same, the vector can move around, it doesn’t have a fixed origin. Computer Science: Ordered list of numbers. Order Matteers Mathematics:

Consider vectors as an arrow pointing out from the origin of an XY plane, the physics student perspective. You can get the Ordered list of numbers, the Computer Science Student’s perspective by getting the coordinates of the arrow.

Every vector gives us only one pair of numbers and vice versa.

Vector Addition:

To add 2 vectors, move the second vector so that it’s tail sits on the head of the first vector. Now the result of the addition is the vector drawn from the tail of the first vector to the head of the second vector.

The direction and length should not be altered when moving the vector

Why is it this way???

Consider the physics perspective, a vector is a length and direction, so when you move to the head of the first vector, and then move in the length and direction of the second vector you get the sum of both the vectors. So In Computer Science perspective, the coordinates of the corresponding plane are added, in a single step to provide the resultant sum.

Vector Multiplication:

Think of it as stretching the vector with the number you are multiplying. The length of vector gets altered, but the direction remains the same.

The direction vector can only be reversed when you multiply it by -1. Otherwise the direction remains unchanged.

This process is called Scaling the vector. The number that is multiplied with the vector is called Scalar.