What is the Difference Between Matrix Notation and Abstract Matrix Notation?

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SUMMARY

The discussion clarifies the distinction between "matrix notation" and "abstract matrix notation." Matrix notation involves using a specific basis for the vector space, represented as a two-dimensional array of coefficients. In contrast, abstract matrix notation does not rely on a specific basis, allowing for a more generalized representation. For example, the operation of premultiplying a vector by a matrix is expressed in matrix notation as &Sigmaj Aij xj = yi, while in abstract matrix notation, it is simplified to A x = y.

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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
 
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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
 

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