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Matrices, although great for computers, are often complicated and unintuitive. This blog was my first insight into an alternative symbolic interpretation for Linear Algebra. It has often led to problems and complicated equations being represented with far more simplicity. As well as teaching me to be more flexible and creative with my own notations.

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Agreed. The graphical notation elegantly demonstrates that a lot of symbolic manipulation just boils down to pushing parts of a formula around until they fit a specific pattern, so that you can apply an identity and replace it with a different pattern.

> It has often led to problems and complicated equations being represented with far more simplicity.

How? AFAICT, the string diagram contains far too much incidental information for doing linear algebra. It contains even more information that a fully parenthesized tree of additions because it even contains information about how to evaluate duplicated expressions (eg. it tells if in (x+y)+(x+y) you should evaluate (x+y) twice or only once and then reuse the value). If we write a string diagram as a normal linear system the whole question of fullness and faithfulness would be dead obvious.

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