The best way of visualizing vectors and vector-matrix multiplications

After going through 3Blue1Brown’s first few videos of the Essence of Linear Algebra series, I finally understood the meaning behind various concepts of Linear Algebra such as vectors, matrix and matrix multiplication. Up to to this point, I knew the how to do the calculations, but never understood what those calculations meant.

Here’s how to visualize it:

• Think of a n- dimensional vector as representing a point in a n-dimensional space.

• As for matrix multiplication, think of it as how a matrix, stretches the coordinate system itself.