I was surprised to learn, given the inelegance of much of Matlab, that it was explicitly influenced by APL. See the blue callout box at

http://www.mathworks.com/company/newsletters/news_notes/clev...

which shows part of a 1983 plan for Matlab:

"Combining the technology of 1) mice and windows, 2) matrix and APL environments, and 3) direct manipulation, will do for engineers what Lotus 1-2-3 has done for the business world."

Ulf Grenander, the Brown University mathematician who invented statistical pattern theory, once used APL, but moved to Matlab for his expository book on pattern theory:

http://books.google.com/books?id=lxBDcFvFFvsC&pg=PA146&#...

I agree that the vectorized operations in Matlab are good at lifting computational ideas out of the fog of nested for loops. It is more compact to represent some matrix algebra in Matlab notation than in ordinary matrix notation, as anyone who has read Golub and van Loan knows.

It's weird to proclaim, but this concise notation can be as freeing for certain problems as Prolog's declarative transformations, and functional composition in Lisp.