Abstract Matrix Notation

[hell18]

I've been doing some computational methods work, using matrix notation. I was just wondering what the difference is between matrix notation and abstract matrix notation?

thanks

[Hurkyl]

I don't think I've seen that term used before, but a brief search on the web on those terms confirms my initial thought.


"Matrix notation" is when you have selected a particular basis (bases) for the vector space (spaces) upon which you're working, and matrices are written as a 2 dimensional array of coefficients with respect to those bases.

"Abstract matrix notation" is when you have not done the above.


For example, suppose you premultiply a vector by a matrix to yield another vector.

In matrix notation, it might look like:

&Sigmaj Aij xj = yi

In abstract matrix notation, it might look like:

A x = y