From: 3blue1brown
The utility of linear algebra largely stems from its capacity to translate between different perspectives of vectors, such as geometric arrows and lists of numbers [00:08:42].
Data Analysis
Linear algebra provides a visual way to conceptualize lists of numbers, which can clarify patterns in data and offer a global view of operations [00:08:50].
Modeling Data as Vectors
In data analysis, features can be modeled as vectors [00:01:12]. For instance, in house price analytics, a house might be modeled as a two-dimensional vector where the first number represents square footage and the second represents price [00:00:55]. The order of these numbers matters [00:01:09]. In this context, “vector” is essentially a synonym for an ordered list [00:01:15].
Computer Graphics
Linear algebra offers physicists and computer graphics programmers a language to describe space and its manipulation using numbers that can be processed by computers [00:09:00].
Animation and Visual Representation
When creating mathematical animations, the process typically involves conceptualizing the spatial movements first, then using the computer to numerically represent these movements to determine pixel placement on screen [00:09:12]. This process heavily relies on linear algebra understanding [00:09:23].