I am not sure it is a good idea that using music as an analogy of mathematics. But let me try it. Most of the music is combination of notes. These notes are not alone. We call a sound if it is alone. If we make sounds together in particular sequence, they become a music. Even I could make a C sound by a piano. But, music is different. Make a C sound by typing a key is an analogy to that we could add two numbers. We can't start the music or mathematics if we don't have this basis. These are fundamental, but, if we made a harmony or thought about vectors, they reach to another level. One sound and a music are different. One scaler operation and a matrix-vector operation are different as well. I think a deep insight of linear algebra comes from like that. Some of the music people might complain this analogy, but, some music are quite mathematical for me, like Bach's musical offering (inverse operation, recursive, infinite), I just think about the analogy.
Well, I would like to say please don't hate linear algebra or matrix because it sounds awkward. I found some kind of entrance of this harmony, so I am writing this article.
I think it is better to stop here and making a new section.
19 hours ago