
Vectors are scaled basis vectors
Hi everyone!
I wanted to share this quick thought that has really helped me with linear algebra;
Let's say: P = (1, 0)
This vector/point is simply the result of scaling the basis vectors ihat [1, 0] and jhat [0, 1]:
Now, if we apply a transformation to the basis vectors, let's say a 90 degree rotation, the same process applies. For example, after the transformations each basis vector lands at column, ihat [0, 1], jhat [-1, 0].
Scaling this with our vector, [1, 0] gives us [0, 1].
So, a transformation transforms the basis vectors and our vector scales it, that's it :)
Enjoy!