Hello I am engineering student. I need help understanding basic of matrix plotting.
Currently I am learning about vectors and I wonder how they are represented by a matrix.
Suppose we have a 2D vector it will be 2x1 matrix and can be simply plotted by taking first row on x axis and second row on y axis.
But, what about 2x2 matrix? I know it can be use for transformation of a vector.
I am curious about what information it holds? like is it contain two separate vector as it has two columns. How it can be represented on graph?
I tried some matrix online plotter. But it seemed like they they had error on their plots or error in my understanding! which confused me more about this.
Please help me understand it!
Here's a basic idea. A matrix takes the xy-plane and alters it in some way, whether that be stretching, shrinking, rotating, etc. Take the first column of the matrix. That vector is the result when you move the vector $\begin{pmatrix} 1 \\ 0 \end{pmatrix}$ to that first column vector. Similarly, the second column vector is the result when you move the vector $\begin{pmatrix} 0 \\ 1 \end{pmatrix}$ to that second column vector. In this way, you stretch space in some way.
It's hard to visualize without ... well, a visual. I urge you to watch this video from 3Blue1Brown that clearly expresses what exactly 2x2 matrices are and how they morph space.