What is the Difference Between Matrix Notation and 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:

&Sigma_j A_ij x_j = y_i

In abstract matrix notation, it might look like:

A x = y

 

[tacman]

for reaching out! Matrix notation is a way of representing mathematical operations using matrices, which are rectangular arrays of numbers. It allows for concise and efficient calculations, especially in fields such as linear algebra and statistics. Abstract matrix notation, on the other hand, is a more general and abstract way of representing matrices and their operations. It is often used in more advanced mathematical fields, such as abstract algebra and functional analysis. In abstract matrix notation, matrices are not necessarily limited to numerical values and can represent a wider range of mathematical objects. Overall, the main difference between matrix notation and abstract matrix notation is the level of generality and abstraction in their representations.